4304 lines
337 KiB
Python
4304 lines
337 KiB
Python
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from sympy.concrete.summations import Sum
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from sympy.core.function import expand
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from sympy.core.numbers import (I, Rational, pi)
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from sympy.core.singleton import S
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from sympy.core.symbol import symbols
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from sympy.functions.elementary.exponential import exp
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.functions.elementary.trigonometric import (cos, sin)
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from sympy.matrices.dense import Matrix
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from sympy.abc import alpha, beta, gamma, j, m
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from sympy.physics.quantum import hbar, represent, Commutator, InnerProduct
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from sympy.physics.quantum.qapply import qapply
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from sympy.physics.quantum.tensorproduct import TensorProduct
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from sympy.physics.quantum.cg import CG
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from sympy.physics.quantum.spin import (
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Jx, Jy, Jz, Jplus, Jminus, J2,
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JxBra, JyBra, JzBra,
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JxKet, JyKet, JzKet,
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JxKetCoupled, JyKetCoupled, JzKetCoupled,
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couple, uncouple,
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Rotation, WignerD
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)
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from sympy.testing.pytest import raises, slow
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j1, j2, j3, j4, m1, m2, m3, m4 = symbols('j1:5 m1:5')
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j12, j13, j24, j34, j123, j134, mi, mi1, mp = symbols(
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'j12 j13 j24 j34 j123 j134 mi mi1 mp')
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def test_represent_spin_operators():
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assert represent(Jx) == hbar*Matrix([[0, 1], [1, 0]])/2
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assert represent(
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Jx, j=1) == hbar*sqrt(2)*Matrix([[0, 1, 0], [1, 0, 1], [0, 1, 0]])/2
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assert represent(Jy) == hbar*I*Matrix([[0, -1], [1, 0]])/2
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assert represent(Jy, j=1) == hbar*I*sqrt(2)*Matrix([[0, -1, 0], [1,
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0, -1], [0, 1, 0]])/2
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assert represent(Jz) == hbar*Matrix([[1, 0], [0, -1]])/2
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assert represent(
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Jz, j=1) == hbar*Matrix([[1, 0, 0], [0, 0, 0], [0, 0, -1]])
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def test_represent_spin_states():
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# Jx basis
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assert represent(JxKet(S.Half, S.Half), basis=Jx) == Matrix([1, 0])
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assert represent(JxKet(S.Half, Rational(-1, 2)), basis=Jx) == Matrix([0, 1])
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assert represent(JxKet(1, 1), basis=Jx) == Matrix([1, 0, 0])
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assert represent(JxKet(1, 0), basis=Jx) == Matrix([0, 1, 0])
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assert represent(JxKet(1, -1), basis=Jx) == Matrix([0, 0, 1])
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assert represent(
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JyKet(S.Half, S.Half), basis=Jx) == Matrix([exp(-I*pi/4), 0])
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assert represent(
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JyKet(S.Half, Rational(-1, 2)), basis=Jx) == Matrix([0, exp(I*pi/4)])
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assert represent(JyKet(1, 1), basis=Jx) == Matrix([-I, 0, 0])
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assert represent(JyKet(1, 0), basis=Jx) == Matrix([0, 1, 0])
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assert represent(JyKet(1, -1), basis=Jx) == Matrix([0, 0, I])
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assert represent(
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JzKet(S.Half, S.Half), basis=Jx) == sqrt(2)*Matrix([-1, 1])/2
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assert represent(
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JzKet(S.Half, Rational(-1, 2)), basis=Jx) == sqrt(2)*Matrix([-1, -1])/2
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assert represent(JzKet(1, 1), basis=Jx) == Matrix([1, -sqrt(2), 1])/2
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assert represent(JzKet(1, 0), basis=Jx) == sqrt(2)*Matrix([1, 0, -1])/2
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assert represent(JzKet(1, -1), basis=Jx) == Matrix([1, sqrt(2), 1])/2
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# Jy basis
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assert represent(
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JxKet(S.Half, S.Half), basis=Jy) == Matrix([exp(I*pi*Rational(-3, 4)), 0])
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assert represent(
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JxKet(S.Half, Rational(-1, 2)), basis=Jy) == Matrix([0, exp(I*pi*Rational(3, 4))])
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assert represent(JxKet(1, 1), basis=Jy) == Matrix([I, 0, 0])
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assert represent(JxKet(1, 0), basis=Jy) == Matrix([0, 1, 0])
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assert represent(JxKet(1, -1), basis=Jy) == Matrix([0, 0, -I])
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assert represent(JyKet(S.Half, S.Half), basis=Jy) == Matrix([1, 0])
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assert represent(JyKet(S.Half, Rational(-1, 2)), basis=Jy) == Matrix([0, 1])
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assert represent(JyKet(1, 1), basis=Jy) == Matrix([1, 0, 0])
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assert represent(JyKet(1, 0), basis=Jy) == Matrix([0, 1, 0])
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assert represent(JyKet(1, -1), basis=Jy) == Matrix([0, 0, 1])
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assert represent(
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JzKet(S.Half, S.Half), basis=Jy) == sqrt(2)*Matrix([-1, I])/2
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assert represent(
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JzKet(S.Half, Rational(-1, 2)), basis=Jy) == sqrt(2)*Matrix([I, -1])/2
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assert represent(JzKet(1, 1), basis=Jy) == Matrix([1, -I*sqrt(2), -1])/2
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assert represent(
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JzKet(1, 0), basis=Jy) == Matrix([-sqrt(2)*I, 0, -sqrt(2)*I])/2
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assert represent(JzKet(1, -1), basis=Jy) == Matrix([-1, -sqrt(2)*I, 1])/2
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# Jz basis
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assert represent(
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JxKet(S.Half, S.Half), basis=Jz) == sqrt(2)*Matrix([1, 1])/2
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assert represent(
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JxKet(S.Half, Rational(-1, 2)), basis=Jz) == sqrt(2)*Matrix([-1, 1])/2
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assert represent(JxKet(1, 1), basis=Jz) == Matrix([1, sqrt(2), 1])/2
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assert represent(JxKet(1, 0), basis=Jz) == sqrt(2)*Matrix([-1, 0, 1])/2
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assert represent(JxKet(1, -1), basis=Jz) == Matrix([1, -sqrt(2), 1])/2
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assert represent(
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JyKet(S.Half, S.Half), basis=Jz) == sqrt(2)*Matrix([-1, -I])/2
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assert represent(
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JyKet(S.Half, Rational(-1, 2)), basis=Jz) == sqrt(2)*Matrix([-I, -1])/2
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assert represent(JyKet(1, 1), basis=Jz) == Matrix([1, sqrt(2)*I, -1])/2
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assert represent(JyKet(1, 0), basis=Jz) == sqrt(2)*Matrix([I, 0, I])/2
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assert represent(JyKet(1, -1), basis=Jz) == Matrix([-1, sqrt(2)*I, 1])/2
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assert represent(JzKet(S.Half, S.Half), basis=Jz) == Matrix([1, 0])
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assert represent(JzKet(S.Half, Rational(-1, 2)), basis=Jz) == Matrix([0, 1])
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assert represent(JzKet(1, 1), basis=Jz) == Matrix([1, 0, 0])
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assert represent(JzKet(1, 0), basis=Jz) == Matrix([0, 1, 0])
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assert represent(JzKet(1, -1), basis=Jz) == Matrix([0, 0, 1])
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def test_represent_uncoupled_states():
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# Jx basis
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assert represent(TensorProduct(JxKet(S.Half, S.Half), JxKet(S.Half, S.Half)), basis=Jx) == \
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Matrix([1, 0, 0, 0])
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assert represent(TensorProduct(JxKet(S.Half, S.Half), JxKet(S.Half, Rational(-1, 2))), basis=Jx) == \
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Matrix([0, 1, 0, 0])
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assert represent(TensorProduct(JxKet(S.Half, Rational(-1, 2)), JxKet(S.Half, S.Half)), basis=Jx) == \
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Matrix([0, 0, 1, 0])
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assert represent(TensorProduct(JxKet(S.Half, Rational(-1, 2)), JxKet(S.Half, Rational(-1, 2))), basis=Jx) == \
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Matrix([0, 0, 0, 1])
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assert represent(TensorProduct(JyKet(S.Half, S.Half), JyKet(S.Half, S.Half)), basis=Jx) == \
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Matrix([-I, 0, 0, 0])
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assert represent(TensorProduct(JyKet(S.Half, S.Half), JyKet(S.Half, Rational(-1, 2))), basis=Jx) == \
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Matrix([0, 1, 0, 0])
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assert represent(TensorProduct(JyKet(S.Half, Rational(-1, 2)), JyKet(S.Half, S.Half)), basis=Jx) == \
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Matrix([0, 0, 1, 0])
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assert represent(TensorProduct(JyKet(S.Half, Rational(-1, 2)), JyKet(S.Half, Rational(-1, 2))), basis=Jx) == \
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Matrix([0, 0, 0, I])
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assert represent(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), basis=Jx) == \
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Matrix([S.Half, Rational(-1, 2), Rational(-1, 2), S.Half])
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assert represent(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), basis=Jx) == \
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Matrix([S.Half, S.Half, Rational(-1, 2), Rational(-1, 2)])
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assert represent(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), basis=Jx) == \
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Matrix([S.Half, Rational(-1, 2), S.Half, Rational(-1, 2)])
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assert represent(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), basis=Jx) == \
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Matrix([S.Half, S.Half, S.Half, S.Half])
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# Jy basis
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assert represent(TensorProduct(JxKet(S.Half, S.Half), JxKet(S.Half, S.Half)), basis=Jy) == \
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Matrix([I, 0, 0, 0])
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assert represent(TensorProduct(JxKet(S.Half, S.Half), JxKet(S.Half, Rational(-1, 2))), basis=Jy) == \
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Matrix([0, 1, 0, 0])
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assert represent(TensorProduct(JxKet(S.Half, Rational(-1, 2)), JxKet(S.Half, S.Half)), basis=Jy) == \
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Matrix([0, 0, 1, 0])
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assert represent(TensorProduct(JxKet(S.Half, Rational(-1, 2)), JxKet(S.Half, Rational(-1, 2))), basis=Jy) == \
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Matrix([0, 0, 0, -I])
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assert represent(TensorProduct(JyKet(S.Half, S.Half), JyKet(S.Half, S.Half)), basis=Jy) == \
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Matrix([1, 0, 0, 0])
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assert represent(TensorProduct(JyKet(S.Half, S.Half), JyKet(S.Half, Rational(-1, 2))), basis=Jy) == \
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Matrix([0, 1, 0, 0])
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assert represent(TensorProduct(JyKet(S.Half, Rational(-1, 2)), JyKet(S.Half, S.Half)), basis=Jy) == \
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Matrix([0, 0, 1, 0])
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assert represent(TensorProduct(JyKet(S.Half, Rational(-1, 2)), JyKet(S.Half, Rational(-1, 2))), basis=Jy) == \
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Matrix([0, 0, 0, 1])
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assert represent(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), basis=Jy) == \
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Matrix([S.Half, -I/2, -I/2, Rational(-1, 2)])
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assert represent(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), basis=Jy) == \
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Matrix([-I/2, S.Half, Rational(-1, 2), -I/2])
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assert represent(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), basis=Jy) == \
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Matrix([-I/2, Rational(-1, 2), S.Half, -I/2])
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assert represent(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), basis=Jy) == \
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Matrix([Rational(-1, 2), -I/2, -I/2, S.Half])
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# Jz basis
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assert represent(TensorProduct(JxKet(S.Half, S.Half), JxKet(S.Half, S.Half)), basis=Jz) == \
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Matrix([S.Half, S.Half, S.Half, S.Half])
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assert represent(TensorProduct(JxKet(S.Half, S.Half), JxKet(S.Half, Rational(-1, 2))), basis=Jz) == \
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Matrix([Rational(-1, 2), S.Half, Rational(-1, 2), S.Half])
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assert represent(TensorProduct(JxKet(S.Half, Rational(-1, 2)), JxKet(S.Half, S.Half)), basis=Jz) == \
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Matrix([Rational(-1, 2), Rational(-1, 2), S.Half, S.Half])
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assert represent(TensorProduct(JxKet(S.Half, Rational(-1, 2)), JxKet(S.Half, Rational(-1, 2))), basis=Jz) == \
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Matrix([S.Half, Rational(-1, 2), Rational(-1, 2), S.Half])
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assert represent(TensorProduct(JyKet(S.Half, S.Half), JyKet(S.Half, S.Half)), basis=Jz) == \
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Matrix([S.Half, I/2, I/2, Rational(-1, 2)])
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assert represent(TensorProduct(JyKet(S.Half, S.Half), JyKet(S.Half, Rational(-1, 2))), basis=Jz) == \
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Matrix([I/2, S.Half, Rational(-1, 2), I/2])
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assert represent(TensorProduct(JyKet(S.Half, Rational(-1, 2)), JyKet(S.Half, S.Half)), basis=Jz) == \
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Matrix([I/2, Rational(-1, 2), S.Half, I/2])
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assert represent(TensorProduct(JyKet(S.Half, Rational(-1, 2)), JyKet(S.Half, Rational(-1, 2))), basis=Jz) == \
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Matrix([Rational(-1, 2), I/2, I/2, S.Half])
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assert represent(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), basis=Jz) == \
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Matrix([1, 0, 0, 0])
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assert represent(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), basis=Jz) == \
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Matrix([0, 1, 0, 0])
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assert represent(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), basis=Jz) == \
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Matrix([0, 0, 1, 0])
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assert represent(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), basis=Jz) == \
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Matrix([0, 0, 0, 1])
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def test_represent_coupled_states():
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# Jx basis
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assert represent(JxKetCoupled(0, 0, (S.Half, S.Half)), basis=Jx) == \
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Matrix([1, 0, 0, 0])
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assert represent(JxKetCoupled(1, 1, (S.Half, S.Half)), basis=Jx) == \
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Matrix([0, 1, 0, 0])
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assert represent(JxKetCoupled(1, 0, (S.Half, S.Half)), basis=Jx) == \
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Matrix([0, 0, 1, 0])
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assert represent(JxKetCoupled(1, -1, (S.Half, S.Half)), basis=Jx) == \
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Matrix([0, 0, 0, 1])
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assert represent(JyKetCoupled(0, 0, (S.Half, S.Half)), basis=Jx) == \
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Matrix([1, 0, 0, 0])
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assert represent(JyKetCoupled(1, 1, (S.Half, S.Half)), basis=Jx) == \
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Matrix([0, -I, 0, 0])
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assert represent(JyKetCoupled(1, 0, (S.Half, S.Half)), basis=Jx) == \
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Matrix([0, 0, 1, 0])
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assert represent(JyKetCoupled(1, -1, (S.Half, S.Half)), basis=Jx) == \
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Matrix([0, 0, 0, I])
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assert represent(JzKetCoupled(0, 0, (S.Half, S.Half)), basis=Jx) == \
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Matrix([1, 0, 0, 0])
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assert represent(JzKetCoupled(1, 1, (S.Half, S.Half)), basis=Jx) == \
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Matrix([0, S.Half, -sqrt(2)/2, S.Half])
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assert represent(JzKetCoupled(1, 0, (S.Half, S.Half)), basis=Jx) == \
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Matrix([0, sqrt(2)/2, 0, -sqrt(2)/2])
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assert represent(JzKetCoupled(1, -1, (S.Half, S.Half)), basis=Jx) == \
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Matrix([0, S.Half, sqrt(2)/2, S.Half])
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# Jy basis
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assert represent(JxKetCoupled(0, 0, (S.Half, S.Half)), basis=Jy) == \
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Matrix([1, 0, 0, 0])
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assert represent(JxKetCoupled(1, 1, (S.Half, S.Half)), basis=Jy) == \
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Matrix([0, I, 0, 0])
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assert represent(JxKetCoupled(1, 0, (S.Half, S.Half)), basis=Jy) == \
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Matrix([0, 0, 1, 0])
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assert represent(JxKetCoupled(1, -1, (S.Half, S.Half)), basis=Jy) == \
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Matrix([0, 0, 0, -I])
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assert represent(JyKetCoupled(0, 0, (S.Half, S.Half)), basis=Jy) == \
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Matrix([1, 0, 0, 0])
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assert represent(JyKetCoupled(1, 1, (S.Half, S.Half)), basis=Jy) == \
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Matrix([0, 1, 0, 0])
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assert represent(JyKetCoupled(1, 0, (S.Half, S.Half)), basis=Jy) == \
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Matrix([0, 0, 1, 0])
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assert represent(JyKetCoupled(1, -1, (S.Half, S.Half)), basis=Jy) == \
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Matrix([0, 0, 0, 1])
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assert represent(JzKetCoupled(0, 0, (S.Half, S.Half)), basis=Jy) == \
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Matrix([1, 0, 0, 0])
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|
|
assert represent(JzKetCoupled(1, 1, (S.Half, S.Half)), basis=Jy) == \
|
||
|
|
Matrix([0, S.Half, -I*sqrt(2)/2, Rational(-1, 2)])
|
||
|
|
assert represent(JzKetCoupled(1, 0, (S.Half, S.Half)), basis=Jy) == \
|
||
|
|
Matrix([0, -I*sqrt(2)/2, 0, -I*sqrt(2)/2])
|
||
|
|
assert represent(JzKetCoupled(1, -1, (S.Half, S.Half)), basis=Jy) == \
|
||
|
|
Matrix([0, Rational(-1, 2), -I*sqrt(2)/2, S.Half])
|
||
|
|
# Jz basis
|
||
|
|
assert represent(JxKetCoupled(0, 0, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([1, 0, 0, 0])
|
||
|
|
assert represent(JxKetCoupled(1, 1, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([0, S.Half, sqrt(2)/2, S.Half])
|
||
|
|
assert represent(JxKetCoupled(1, 0, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([0, -sqrt(2)/2, 0, sqrt(2)/2])
|
||
|
|
assert represent(JxKetCoupled(1, -1, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([0, S.Half, -sqrt(2)/2, S.Half])
|
||
|
|
assert represent(JyKetCoupled(0, 0, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([1, 0, 0, 0])
|
||
|
|
assert represent(JyKetCoupled(1, 1, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([0, S.Half, I*sqrt(2)/2, Rational(-1, 2)])
|
||
|
|
assert represent(JyKetCoupled(1, 0, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([0, I*sqrt(2)/2, 0, I*sqrt(2)/2])
|
||
|
|
assert represent(JyKetCoupled(1, -1, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([0, Rational(-1, 2), I*sqrt(2)/2, S.Half])
|
||
|
|
assert represent(JzKetCoupled(0, 0, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([1, 0, 0, 0])
|
||
|
|
assert represent(JzKetCoupled(1, 1, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([0, 1, 0, 0])
|
||
|
|
assert represent(JzKetCoupled(1, 0, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([0, 0, 1, 0])
|
||
|
|
assert represent(JzKetCoupled(1, -1, (S.Half, S.Half)), basis=Jz) == \
|
||
|
|
Matrix([0, 0, 0, 1])
|
||
|
|
|
||
|
|
|
||
|
|
def test_represent_rotation():
|
||
|
|
assert represent(Rotation(0, pi/2, 0)) == \
|
||
|
|
Matrix(
|
||
|
|
[[WignerD(
|
||
|
|
S(
|
||
|
|
1)/2, S(
|
||
|
|
1)/2, S(
|
||
|
|
1)/2, 0, pi/2, 0), WignerD(
|
||
|
|
S.Half, S.Half, Rational(-1, 2), 0, pi/2, 0)],
|
||
|
|
[WignerD(S.Half, Rational(-1, 2), S.Half, 0, pi/2, 0), WignerD(S.Half, Rational(-1, 2), Rational(-1, 2), 0, pi/2, 0)]])
|
||
|
|
assert represent(Rotation(0, pi/2, 0), doit=True) == \
|
||
|
|
Matrix([[sqrt(2)/2, -sqrt(2)/2],
|
||
|
|
[sqrt(2)/2, sqrt(2)/2]])
|
||
|
|
|
||
|
|
|
||
|
|
def test_rewrite_same():
|
||
|
|
# Rewrite to same basis
|
||
|
|
assert JxBra(1, 1).rewrite('Jx') == JxBra(1, 1)
|
||
|
|
assert JxBra(j, m).rewrite('Jx') == JxBra(j, m)
|
||
|
|
assert JxKet(1, 1).rewrite('Jx') == JxKet(1, 1)
|
||
|
|
assert JxKet(j, m).rewrite('Jx') == JxKet(j, m)
|
||
|
|
|
||
|
|
|
||
|
|
def test_rewrite_Bra():
|
||
|
|
# Numerical
|
||
|
|
assert JxBra(1, 1).rewrite('Jy') == -I*JyBra(1, 1)
|
||
|
|
assert JxBra(1, 0).rewrite('Jy') == JyBra(1, 0)
|
||
|
|
assert JxBra(1, -1).rewrite('Jy') == I*JyBra(1, -1)
|
||
|
|
assert JxBra(1, 1).rewrite(
|
||
|
|
'Jz') == JzBra(1, 1)/2 + JzBra(1, 0)/sqrt(2) + JzBra(1, -1)/2
|
||
|
|
assert JxBra(
|
||
|
|
1, 0).rewrite('Jz') == -sqrt(2)*JzBra(1, 1)/2 + sqrt(2)*JzBra(1, -1)/2
|
||
|
|
assert JxBra(1, -1).rewrite(
|
||
|
|
'Jz') == JzBra(1, 1)/2 - JzBra(1, 0)/sqrt(2) + JzBra(1, -1)/2
|
||
|
|
assert JyBra(1, 1).rewrite('Jx') == I*JxBra(1, 1)
|
||
|
|
assert JyBra(1, 0).rewrite('Jx') == JxBra(1, 0)
|
||
|
|
assert JyBra(1, -1).rewrite('Jx') == -I*JxBra(1, -1)
|
||
|
|
assert JyBra(1, 1).rewrite(
|
||
|
|
'Jz') == JzBra(1, 1)/2 - sqrt(2)*I*JzBra(1, 0)/2 - JzBra(1, -1)/2
|
||
|
|
assert JyBra(1, 0).rewrite(
|
||
|
|
'Jz') == -sqrt(2)*I*JzBra(1, 1)/2 - sqrt(2)*I*JzBra(1, -1)/2
|
||
|
|
assert JyBra(1, -1).rewrite(
|
||
|
|
'Jz') == -JzBra(1, 1)/2 - sqrt(2)*I*JzBra(1, 0)/2 + JzBra(1, -1)/2
|
||
|
|
assert JzBra(1, 1).rewrite(
|
||
|
|
'Jx') == JxBra(1, 1)/2 - sqrt(2)*JxBra(1, 0)/2 + JxBra(1, -1)/2
|
||
|
|
assert JzBra(
|
||
|
|
1, 0).rewrite('Jx') == sqrt(2)*JxBra(1, 1)/2 - sqrt(2)*JxBra(1, -1)/2
|
||
|
|
assert JzBra(1, -1).rewrite(
|
||
|
|
'Jx') == JxBra(1, 1)/2 + sqrt(2)*JxBra(1, 0)/2 + JxBra(1, -1)/2
|
||
|
|
assert JzBra(1, 1).rewrite(
|
||
|
|
'Jy') == JyBra(1, 1)/2 + sqrt(2)*I*JyBra(1, 0)/2 - JyBra(1, -1)/2
|
||
|
|
assert JzBra(1, 0).rewrite(
|
||
|
|
'Jy') == sqrt(2)*I*JyBra(1, 1)/2 + sqrt(2)*I*JyBra(1, -1)/2
|
||
|
|
assert JzBra(1, -1).rewrite(
|
||
|
|
'Jy') == -JyBra(1, 1)/2 + sqrt(2)*I*JyBra(1, 0)/2 + JyBra(1, -1)/2
|
||
|
|
# Symbolic
|
||
|
|
assert JxBra(j, m).rewrite('Jy') == Sum(
|
||
|
|
WignerD(j, mi, m, pi*Rational(3, 2), 0, 0) * JyBra(j, mi), (mi, -j, j))
|
||
|
|
assert JxBra(j, m).rewrite('Jz') == Sum(
|
||
|
|
WignerD(j, mi, m, 0, pi/2, 0) * JzBra(j, mi), (mi, -j, j))
|
||
|
|
assert JyBra(j, m).rewrite('Jx') == Sum(
|
||
|
|
WignerD(j, mi, m, 0, 0, pi/2) * JxBra(j, mi), (mi, -j, j))
|
||
|
|
assert JyBra(j, m).rewrite('Jz') == Sum(
|
||
|
|
WignerD(j, mi, m, pi*Rational(3, 2), -pi/2, pi/2) * JzBra(j, mi), (mi, -j, j))
|
||
|
|
assert JzBra(j, m).rewrite('Jx') == Sum(
|
||
|
|
WignerD(j, mi, m, 0, pi*Rational(3, 2), 0) * JxBra(j, mi), (mi, -j, j))
|
||
|
|
assert JzBra(j, m).rewrite('Jy') == Sum(
|
||
|
|
WignerD(j, mi, m, pi*Rational(3, 2), pi/2, pi/2) * JyBra(j, mi), (mi, -j, j))
|
||
|
|
|
||
|
|
|
||
|
|
def test_rewrite_Ket():
|
||
|
|
# Numerical
|
||
|
|
assert JxKet(1, 1).rewrite('Jy') == I*JyKet(1, 1)
|
||
|
|
assert JxKet(1, 0).rewrite('Jy') == JyKet(1, 0)
|
||
|
|
assert JxKet(1, -1).rewrite('Jy') == -I*JyKet(1, -1)
|
||
|
|
assert JxKet(1, 1).rewrite(
|
||
|
|
'Jz') == JzKet(1, 1)/2 + JzKet(1, 0)/sqrt(2) + JzKet(1, -1)/2
|
||
|
|
assert JxKet(
|
||
|
|
1, 0).rewrite('Jz') == -sqrt(2)*JzKet(1, 1)/2 + sqrt(2)*JzKet(1, -1)/2
|
||
|
|
assert JxKet(1, -1).rewrite(
|
||
|
|
'Jz') == JzKet(1, 1)/2 - JzKet(1, 0)/sqrt(2) + JzKet(1, -1)/2
|
||
|
|
assert JyKet(1, 1).rewrite('Jx') == -I*JxKet(1, 1)
|
||
|
|
assert JyKet(1, 0).rewrite('Jx') == JxKet(1, 0)
|
||
|
|
assert JyKet(1, -1).rewrite('Jx') == I*JxKet(1, -1)
|
||
|
|
assert JyKet(1, 1).rewrite(
|
||
|
|
'Jz') == JzKet(1, 1)/2 + sqrt(2)*I*JzKet(1, 0)/2 - JzKet(1, -1)/2
|
||
|
|
assert JyKet(1, 0).rewrite(
|
||
|
|
'Jz') == sqrt(2)*I*JzKet(1, 1)/2 + sqrt(2)*I*JzKet(1, -1)/2
|
||
|
|
assert JyKet(1, -1).rewrite(
|
||
|
|
'Jz') == -JzKet(1, 1)/2 + sqrt(2)*I*JzKet(1, 0)/2 + JzKet(1, -1)/2
|
||
|
|
assert JzKet(1, 1).rewrite(
|
||
|
|
'Jx') == JxKet(1, 1)/2 - sqrt(2)*JxKet(1, 0)/2 + JxKet(1, -1)/2
|
||
|
|
assert JzKet(
|
||
|
|
1, 0).rewrite('Jx') == sqrt(2)*JxKet(1, 1)/2 - sqrt(2)*JxKet(1, -1)/2
|
||
|
|
assert JzKet(1, -1).rewrite(
|
||
|
|
'Jx') == JxKet(1, 1)/2 + sqrt(2)*JxKet(1, 0)/2 + JxKet(1, -1)/2
|
||
|
|
assert JzKet(1, 1).rewrite(
|
||
|
|
'Jy') == JyKet(1, 1)/2 - sqrt(2)*I*JyKet(1, 0)/2 - JyKet(1, -1)/2
|
||
|
|
assert JzKet(1, 0).rewrite(
|
||
|
|
'Jy') == -sqrt(2)*I*JyKet(1, 1)/2 - sqrt(2)*I*JyKet(1, -1)/2
|
||
|
|
assert JzKet(1, -1).rewrite(
|
||
|
|
'Jy') == -JyKet(1, 1)/2 - sqrt(2)*I*JyKet(1, 0)/2 + JyKet(1, -1)/2
|
||
|
|
# Symbolic
|
||
|
|
assert JxKet(j, m).rewrite('Jy') == Sum(
|
||
|
|
WignerD(j, mi, m, pi*Rational(3, 2), 0, 0) * JyKet(j, mi), (mi, -j, j))
|
||
|
|
assert JxKet(j, m).rewrite('Jz') == Sum(
|
||
|
|
WignerD(j, mi, m, 0, pi/2, 0) * JzKet(j, mi), (mi, -j, j))
|
||
|
|
assert JyKet(j, m).rewrite('Jx') == Sum(
|
||
|
|
WignerD(j, mi, m, 0, 0, pi/2) * JxKet(j, mi), (mi, -j, j))
|
||
|
|
assert JyKet(j, m).rewrite('Jz') == Sum(
|
||
|
|
WignerD(j, mi, m, pi*Rational(3, 2), -pi/2, pi/2) * JzKet(j, mi), (mi, -j, j))
|
||
|
|
assert JzKet(j, m).rewrite('Jx') == Sum(
|
||
|
|
WignerD(j, mi, m, 0, pi*Rational(3, 2), 0) * JxKet(j, mi), (mi, -j, j))
|
||
|
|
assert JzKet(j, m).rewrite('Jy') == Sum(
|
||
|
|
WignerD(j, mi, m, pi*Rational(3, 2), pi/2, pi/2) * JyKet(j, mi), (mi, -j, j))
|
||
|
|
|
||
|
|
|
||
|
|
def test_rewrite_uncoupled_state():
|
||
|
|
# Numerical
|
||
|
|
assert TensorProduct(JyKet(1, 1), JxKet(
|
||
|
|
1, 1)).rewrite('Jx') == -I*TensorProduct(JxKet(1, 1), JxKet(1, 1))
|
||
|
|
assert TensorProduct(JyKet(1, 0), JxKet(
|
||
|
|
1, 1)).rewrite('Jx') == TensorProduct(JxKet(1, 0), JxKet(1, 1))
|
||
|
|
assert TensorProduct(JyKet(1, -1), JxKet(
|
||
|
|
1, 1)).rewrite('Jx') == I*TensorProduct(JxKet(1, -1), JxKet(1, 1))
|
||
|
|
assert TensorProduct(JzKet(1, 1), JxKet(1, 1)).rewrite('Jx') == \
|
||
|
|
TensorProduct(JxKet(1, -1), JxKet(1, 1))/2 - sqrt(2)*TensorProduct(JxKet(
|
||
|
|
1, 0), JxKet(1, 1))/2 + TensorProduct(JxKet(1, 1), JxKet(1, 1))/2
|
||
|
|
assert TensorProduct(JzKet(1, 0), JxKet(1, 1)).rewrite('Jx') == \
|
||
|
|
-sqrt(2)*TensorProduct(JxKet(1, -1), JxKet(1, 1))/2 + sqrt(
|
||
|
|
2)*TensorProduct(JxKet(1, 1), JxKet(1, 1))/2
|
||
|
|
assert TensorProduct(JzKet(1, -1), JxKet(1, 1)).rewrite('Jx') == \
|
||
|
|
TensorProduct(JxKet(1, -1), JxKet(1, 1))/2 + sqrt(2)*TensorProduct(JxKet(1, 0), JxKet(1, 1))/2 + TensorProduct(JxKet(1, 1), JxKet(1, 1))/2
|
||
|
|
assert TensorProduct(JxKet(1, 1), JyKet(
|
||
|
|
1, 1)).rewrite('Jy') == I*TensorProduct(JyKet(1, 1), JyKet(1, 1))
|
||
|
|
assert TensorProduct(JxKet(1, 0), JyKet(
|
||
|
|
1, 1)).rewrite('Jy') == TensorProduct(JyKet(1, 0), JyKet(1, 1))
|
||
|
|
assert TensorProduct(JxKet(1, -1), JyKet(
|
||
|
|
1, 1)).rewrite('Jy') == -I*TensorProduct(JyKet(1, -1), JyKet(1, 1))
|
||
|
|
assert TensorProduct(JzKet(1, 1), JyKet(1, 1)).rewrite('Jy') == \
|
||
|
|
-TensorProduct(JyKet(1, -1), JyKet(1, 1))/2 - sqrt(2)*I*TensorProduct(JyKet(1, 0), JyKet(1, 1))/2 + TensorProduct(JyKet(1, 1), JyKet(1, 1))/2
|
||
|
|
assert TensorProduct(JzKet(1, 0), JyKet(1, 1)).rewrite('Jy') == \
|
||
|
|
-sqrt(2)*I*TensorProduct(JyKet(1, -1), JyKet(
|
||
|
|
1, 1))/2 - sqrt(2)*I*TensorProduct(JyKet(1, 1), JyKet(1, 1))/2
|
||
|
|
assert TensorProduct(JzKet(1, -1), JyKet(1, 1)).rewrite('Jy') == \
|
||
|
|
TensorProduct(JyKet(1, -1), JyKet(1, 1))/2 - sqrt(2)*I*TensorProduct(JyKet(1, 0), JyKet(1, 1))/2 - TensorProduct(JyKet(1, 1), JyKet(1, 1))/2
|
||
|
|
assert TensorProduct(JxKet(1, 1), JzKet(1, 1)).rewrite('Jz') == \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(1, 1))/2 + sqrt(2)*TensorProduct(JzKet(1, 0), JzKet(1, 1))/2 + TensorProduct(JzKet(1, 1), JzKet(1, 1))/2
|
||
|
|
assert TensorProduct(JxKet(1, 0), JzKet(1, 1)).rewrite('Jz') == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, -1), JzKet(
|
||
|
|
1, 1))/2 - sqrt(2)*TensorProduct(JzKet(1, 1), JzKet(1, 1))/2
|
||
|
|
assert TensorProduct(JxKet(1, -1), JzKet(1, 1)).rewrite('Jz') == \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(1, 1))/2 - sqrt(2)*TensorProduct(JzKet(1, 0), JzKet(1, 1))/2 + TensorProduct(JzKet(1, 1), JzKet(1, 1))/2
|
||
|
|
assert TensorProduct(JyKet(1, 1), JzKet(1, 1)).rewrite('Jz') == \
|
||
|
|
-TensorProduct(JzKet(1, -1), JzKet(1, 1))/2 + sqrt(2)*I*TensorProduct(JzKet(1, 0), JzKet(1, 1))/2 + TensorProduct(JzKet(1, 1), JzKet(1, 1))/2
|
||
|
|
assert TensorProduct(JyKet(1, 0), JzKet(1, 1)).rewrite('Jz') == \
|
||
|
|
sqrt(2)*I*TensorProduct(JzKet(1, -1), JzKet(
|
||
|
|
1, 1))/2 + sqrt(2)*I*TensorProduct(JzKet(1, 1), JzKet(1, 1))/2
|
||
|
|
assert TensorProduct(JyKet(1, -1), JzKet(1, 1)).rewrite('Jz') == \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(1, 1))/2 + sqrt(2)*I*TensorProduct(JzKet(1, 0), JzKet(1, 1))/2 - TensorProduct(JzKet(1, 1), JzKet(1, 1))/2
|
||
|
|
# Symbolic
|
||
|
|
assert TensorProduct(JyKet(j1, m1), JxKet(j2, m2)).rewrite('Jy') == \
|
||
|
|
TensorProduct(JyKet(j1, m1), Sum(
|
||
|
|
WignerD(j2, mi, m2, pi*Rational(3, 2), 0, 0) * JyKet(j2, mi), (mi, -j2, j2)))
|
||
|
|
assert TensorProduct(JzKet(j1, m1), JxKet(j2, m2)).rewrite('Jz') == \
|
||
|
|
TensorProduct(JzKet(j1, m1), Sum(
|
||
|
|
WignerD(j2, mi, m2, 0, pi/2, 0) * JzKet(j2, mi), (mi, -j2, j2)))
|
||
|
|
assert TensorProduct(JxKet(j1, m1), JyKet(j2, m2)).rewrite('Jx') == \
|
||
|
|
TensorProduct(JxKet(j1, m1), Sum(
|
||
|
|
WignerD(j2, mi, m2, 0, 0, pi/2) * JxKet(j2, mi), (mi, -j2, j2)))
|
||
|
|
assert TensorProduct(JzKet(j1, m1), JyKet(j2, m2)).rewrite('Jz') == \
|
||
|
|
TensorProduct(JzKet(j1, m1), Sum(WignerD(
|
||
|
|
j2, mi, m2, pi*Rational(3, 2), -pi/2, pi/2) * JzKet(j2, mi), (mi, -j2, j2)))
|
||
|
|
assert TensorProduct(JxKet(j1, m1), JzKet(j2, m2)).rewrite('Jx') == \
|
||
|
|
TensorProduct(JxKet(j1, m1), Sum(
|
||
|
|
WignerD(j2, mi, m2, 0, pi*Rational(3, 2), 0) * JxKet(j2, mi), (mi, -j2, j2)))
|
||
|
|
assert TensorProduct(JyKet(j1, m1), JzKet(j2, m2)).rewrite('Jy') == \
|
||
|
|
TensorProduct(JyKet(j1, m1), Sum(WignerD(
|
||
|
|
j2, mi, m2, pi*Rational(3, 2), pi/2, pi/2) * JyKet(j2, mi), (mi, -j2, j2)))
|
||
|
|
|
||
|
|
|
||
|
|
def test_rewrite_coupled_state():
|
||
|
|
# Numerical
|
||
|
|
assert JyKetCoupled(0, 0, (S.Half, S.Half)).rewrite('Jx') == \
|
||
|
|
JxKetCoupled(0, 0, (S.Half, S.Half))
|
||
|
|
assert JyKetCoupled(1, 1, (S.Half, S.Half)).rewrite('Jx') == \
|
||
|
|
-I*JxKetCoupled(1, 1, (S.Half, S.Half))
|
||
|
|
assert JyKetCoupled(1, 0, (S.Half, S.Half)).rewrite('Jx') == \
|
||
|
|
JxKetCoupled(1, 0, (S.Half, S.Half))
|
||
|
|
assert JyKetCoupled(1, -1, (S.Half, S.Half)).rewrite('Jx') == \
|
||
|
|
I*JxKetCoupled(1, -1, (S.Half, S.Half))
|
||
|
|
assert JzKetCoupled(0, 0, (S.Half, S.Half)).rewrite('Jx') == \
|
||
|
|
JxKetCoupled(0, 0, (S.Half, S.Half))
|
||
|
|
assert JzKetCoupled(1, 1, (S.Half, S.Half)).rewrite('Jx') == \
|
||
|
|
JxKetCoupled(1, 1, (S.Half, S.Half))/2 - sqrt(2)*JxKetCoupled(1, 0, (
|
||
|
|
S.Half, S.Half))/2 + JxKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JzKetCoupled(1, 0, (S.Half, S.Half)).rewrite('Jx') == \
|
||
|
|
sqrt(2)*JxKetCoupled(1, 1, (S(
|
||
|
|
1)/2, S.Half))/2 - sqrt(2)*JxKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JzKetCoupled(1, -1, (S.Half, S.Half)).rewrite('Jx') == \
|
||
|
|
JxKetCoupled(1, 1, (S.Half, S.Half))/2 + sqrt(2)*JxKetCoupled(1, 0, (
|
||
|
|
S.Half, S.Half))/2 + JxKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JxKetCoupled(0, 0, (S.Half, S.Half)).rewrite('Jy') == \
|
||
|
|
JyKetCoupled(0, 0, (S.Half, S.Half))
|
||
|
|
assert JxKetCoupled(1, 1, (S.Half, S.Half)).rewrite('Jy') == \
|
||
|
|
I*JyKetCoupled(1, 1, (S.Half, S.Half))
|
||
|
|
assert JxKetCoupled(1, 0, (S.Half, S.Half)).rewrite('Jy') == \
|
||
|
|
JyKetCoupled(1, 0, (S.Half, S.Half))
|
||
|
|
assert JxKetCoupled(1, -1, (S.Half, S.Half)).rewrite('Jy') == \
|
||
|
|
-I*JyKetCoupled(1, -1, (S.Half, S.Half))
|
||
|
|
assert JzKetCoupled(0, 0, (S.Half, S.Half)).rewrite('Jy') == \
|
||
|
|
JyKetCoupled(0, 0, (S.Half, S.Half))
|
||
|
|
assert JzKetCoupled(1, 1, (S.Half, S.Half)).rewrite('Jy') == \
|
||
|
|
JyKetCoupled(1, 1, (S.Half, S.Half))/2 - I*sqrt(2)*JyKetCoupled(1, 0, (
|
||
|
|
S.Half, S.Half))/2 - JyKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JzKetCoupled(1, 0, (S.Half, S.Half)).rewrite('Jy') == \
|
||
|
|
-I*sqrt(2)*JyKetCoupled(1, 1, (S.Half, S.Half))/2 - I*sqrt(
|
||
|
|
2)*JyKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JzKetCoupled(1, -1, (S.Half, S.Half)).rewrite('Jy') == \
|
||
|
|
-JyKetCoupled(1, 1, (S.Half, S.Half))/2 - I*sqrt(2)*JyKetCoupled(1, 0, (S.Half, S.Half))/2 + JyKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JxKetCoupled(0, 0, (S.Half, S.Half)).rewrite('Jz') == \
|
||
|
|
JzKetCoupled(0, 0, (S.Half, S.Half))
|
||
|
|
assert JxKetCoupled(1, 1, (S.Half, S.Half)).rewrite('Jz') == \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half))/2 + sqrt(2)*JzKetCoupled(1, 0, (
|
||
|
|
S.Half, S.Half))/2 + JzKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JxKetCoupled(1, 0, (S.Half, S.Half)).rewrite('Jz') == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, 1, (S(
|
||
|
|
1)/2, S.Half))/2 + sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JxKetCoupled(1, -1, (S.Half, S.Half)).rewrite('Jz') == \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half))/2 - sqrt(2)*JzKetCoupled(1, 0, (
|
||
|
|
S.Half, S.Half))/2 + JzKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JyKetCoupled(0, 0, (S.Half, S.Half)).rewrite('Jz') == \
|
||
|
|
JzKetCoupled(0, 0, (S.Half, S.Half))
|
||
|
|
assert JyKetCoupled(1, 1, (S.Half, S.Half)).rewrite('Jz') == \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half))/2 + I*sqrt(2)*JzKetCoupled(1, 0, (
|
||
|
|
S.Half, S.Half))/2 - JzKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JyKetCoupled(1, 0, (S.Half, S.Half)).rewrite('Jz') == \
|
||
|
|
I*sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half))/2 + I*sqrt(
|
||
|
|
2)*JzKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
assert JyKetCoupled(1, -1, (S.Half, S.Half)).rewrite('Jz') == \
|
||
|
|
-JzKetCoupled(1, 1, (S.Half, S.Half))/2 + I*sqrt(2)*JzKetCoupled(1, 0, (S.Half, S.Half))/2 + JzKetCoupled(1, -1, (S.Half, S.Half))/2
|
||
|
|
# Symbolic
|
||
|
|
assert JyKetCoupled(j, m, (j1, j2)).rewrite('Jx') == \
|
||
|
|
Sum(WignerD(j, mi, m, 0, 0, pi/2) * JxKetCoupled(j, mi, (
|
||
|
|
j1, j2)), (mi, -j, j))
|
||
|
|
assert JzKetCoupled(j, m, (j1, j2)).rewrite('Jx') == \
|
||
|
|
Sum(WignerD(j, mi, m, 0, pi*Rational(3, 2), 0) * JxKetCoupled(j, mi, (
|
||
|
|
j1, j2)), (mi, -j, j))
|
||
|
|
assert JxKetCoupled(j, m, (j1, j2)).rewrite('Jy') == \
|
||
|
|
Sum(WignerD(j, mi, m, pi*Rational(3, 2), 0, 0) * JyKetCoupled(j, mi, (
|
||
|
|
j1, j2)), (mi, -j, j))
|
||
|
|
assert JzKetCoupled(j, m, (j1, j2)).rewrite('Jy') == \
|
||
|
|
Sum(WignerD(j, mi, m, pi*Rational(3, 2), pi/2, pi/2) * JyKetCoupled(j,
|
||
|
|
mi, (j1, j2)), (mi, -j, j))
|
||
|
|
assert JxKetCoupled(j, m, (j1, j2)).rewrite('Jz') == \
|
||
|
|
Sum(WignerD(j, mi, m, 0, pi/2, 0) * JzKetCoupled(j, mi, (
|
||
|
|
j1, j2)), (mi, -j, j))
|
||
|
|
assert JyKetCoupled(j, m, (j1, j2)).rewrite('Jz') == \
|
||
|
|
Sum(WignerD(j, mi, m, pi*Rational(3, 2), -pi/2, pi/2) * JzKetCoupled(
|
||
|
|
j, mi, (j1, j2)), (mi, -j, j))
|
||
|
|
|
||
|
|
|
||
|
|
def test_innerproducts_of_rewritten_states():
|
||
|
|
# Numerical
|
||
|
|
assert qapply(JxBra(1, 1)*JxKet(1, 1).rewrite('Jy')).doit() == 1
|
||
|
|
assert qapply(JxBra(1, 0)*JxKet(1, 0).rewrite('Jy')).doit() == 1
|
||
|
|
assert qapply(JxBra(1, -1)*JxKet(1, -1).rewrite('Jy')).doit() == 1
|
||
|
|
assert qapply(JxBra(1, 1)*JxKet(1, 1).rewrite('Jz')).doit() == 1
|
||
|
|
assert qapply(JxBra(1, 0)*JxKet(1, 0).rewrite('Jz')).doit() == 1
|
||
|
|
assert qapply(JxBra(1, -1)*JxKet(1, -1).rewrite('Jz')).doit() == 1
|
||
|
|
assert qapply(JyBra(1, 1)*JyKet(1, 1).rewrite('Jx')).doit() == 1
|
||
|
|
assert qapply(JyBra(1, 0)*JyKet(1, 0).rewrite('Jx')).doit() == 1
|
||
|
|
assert qapply(JyBra(1, -1)*JyKet(1, -1).rewrite('Jx')).doit() == 1
|
||
|
|
assert qapply(JyBra(1, 1)*JyKet(1, 1).rewrite('Jz')).doit() == 1
|
||
|
|
assert qapply(JyBra(1, 0)*JyKet(1, 0).rewrite('Jz')).doit() == 1
|
||
|
|
assert qapply(JyBra(1, -1)*JyKet(1, -1).rewrite('Jz')).doit() == 1
|
||
|
|
assert qapply(JyBra(1, 1)*JyKet(1, 1).rewrite('Jz')).doit() == 1
|
||
|
|
assert qapply(JyBra(1, 0)*JyKet(1, 0).rewrite('Jz')).doit() == 1
|
||
|
|
assert qapply(JyBra(1, -1)*JyKet(1, -1).rewrite('Jz')).doit() == 1
|
||
|
|
assert qapply(JzBra(1, 1)*JzKet(1, 1).rewrite('Jy')).doit() == 1
|
||
|
|
assert qapply(JzBra(1, 0)*JzKet(1, 0).rewrite('Jy')).doit() == 1
|
||
|
|
assert qapply(JzBra(1, -1)*JzKet(1, -1).rewrite('Jy')).doit() == 1
|
||
|
|
assert qapply(JxBra(1, 1)*JxKet(1, 0).rewrite('Jy')).doit() == 0
|
||
|
|
assert qapply(JxBra(1, 1)*JxKet(1, -1).rewrite('Jy')) == 0
|
||
|
|
assert qapply(JxBra(1, 1)*JxKet(1, 0).rewrite('Jz')).doit() == 0
|
||
|
|
assert qapply(JxBra(1, 1)*JxKet(1, -1).rewrite('Jz')) == 0
|
||
|
|
assert qapply(JyBra(1, 1)*JyKet(1, 0).rewrite('Jx')).doit() == 0
|
||
|
|
assert qapply(JyBra(1, 1)*JyKet(1, -1).rewrite('Jx')) == 0
|
||
|
|
assert qapply(JyBra(1, 1)*JyKet(1, 0).rewrite('Jz')).doit() == 0
|
||
|
|
assert qapply(JyBra(1, 1)*JyKet(1, -1).rewrite('Jz')) == 0
|
||
|
|
assert qapply(JzBra(1, 1)*JzKet(1, 0).rewrite('Jx')).doit() == 0
|
||
|
|
assert qapply(JzBra(1, 1)*JzKet(1, -1).rewrite('Jx')) == 0
|
||
|
|
assert qapply(JzBra(1, 1)*JzKet(1, 0).rewrite('Jy')).doit() == 0
|
||
|
|
assert qapply(JzBra(1, 1)*JzKet(1, -1).rewrite('Jy')) == 0
|
||
|
|
assert qapply(JxBra(1, 0)*JxKet(1, 1).rewrite('Jy')) == 0
|
||
|
|
assert qapply(JxBra(1, 0)*JxKet(1, -1).rewrite('Jy')) == 0
|
||
|
|
assert qapply(JxBra(1, 0)*JxKet(1, 1).rewrite('Jz')) == 0
|
||
|
|
assert qapply(JxBra(1, 0)*JxKet(1, -1).rewrite('Jz')) == 0
|
||
|
|
assert qapply(JyBra(1, 0)*JyKet(1, 1).rewrite('Jx')) == 0
|
||
|
|
assert qapply(JyBra(1, 0)*JyKet(1, -1).rewrite('Jx')) == 0
|
||
|
|
assert qapply(JyBra(1, 0)*JyKet(1, 1).rewrite('Jz')) == 0
|
||
|
|
assert qapply(JyBra(1, 0)*JyKet(1, -1).rewrite('Jz')) == 0
|
||
|
|
assert qapply(JzBra(1, 0)*JzKet(1, 1).rewrite('Jx')) == 0
|
||
|
|
assert qapply(JzBra(1, 0)*JzKet(1, -1).rewrite('Jx')) == 0
|
||
|
|
assert qapply(JzBra(1, 0)*JzKet(1, 1).rewrite('Jy')) == 0
|
||
|
|
assert qapply(JzBra(1, 0)*JzKet(1, -1).rewrite('Jy')) == 0
|
||
|
|
assert qapply(JxBra(1, -1)*JxKet(1, 1).rewrite('Jy')) == 0
|
||
|
|
assert qapply(JxBra(1, -1)*JxKet(1, 0).rewrite('Jy')).doit() == 0
|
||
|
|
assert qapply(JxBra(1, -1)*JxKet(1, 1).rewrite('Jz')) == 0
|
||
|
|
assert qapply(JxBra(1, -1)*JxKet(1, 0).rewrite('Jz')).doit() == 0
|
||
|
|
assert qapply(JyBra(1, -1)*JyKet(1, 1).rewrite('Jx')) == 0
|
||
|
|
assert qapply(JyBra(1, -1)*JyKet(1, 0).rewrite('Jx')).doit() == 0
|
||
|
|
assert qapply(JyBra(1, -1)*JyKet(1, 1).rewrite('Jz')) == 0
|
||
|
|
assert qapply(JyBra(1, -1)*JyKet(1, 0).rewrite('Jz')).doit() == 0
|
||
|
|
assert qapply(JzBra(1, -1)*JzKet(1, 1).rewrite('Jx')) == 0
|
||
|
|
assert qapply(JzBra(1, -1)*JzKet(1, 0).rewrite('Jx')).doit() == 0
|
||
|
|
assert qapply(JzBra(1, -1)*JzKet(1, 1).rewrite('Jy')) == 0
|
||
|
|
assert qapply(JzBra(1, -1)*JzKet(1, 0).rewrite('Jy')).doit() == 0
|
||
|
|
|
||
|
|
|
||
|
|
def test_uncouple_2_coupled_states():
|
||
|
|
# j1=1/2, j2=1/2
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple(
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple(
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple(
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple(
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
# j1=1/2, j2=1
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1)) == \
|
||
|
|
expand(uncouple(
|
||
|
|
couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0)) == \
|
||
|
|
expand(uncouple(
|
||
|
|
couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1)) == \
|
||
|
|
expand(uncouple(
|
||
|
|
couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1)) == \
|
||
|
|
expand(uncouple(
|
||
|
|
couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0)) == \
|
||
|
|
expand(uncouple(
|
||
|
|
couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1)) == \
|
||
|
|
expand(uncouple(
|
||
|
|
couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1)) )))
|
||
|
|
# j1=1, j2=1
|
||
|
|
assert TensorProduct(JzKet(1, 1), JzKet(1, 1)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(1, 1), JzKet(1, 1)) )))
|
||
|
|
assert TensorProduct(JzKet(1, 1), JzKet(1, 0)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(1, 1), JzKet(1, 0)) )))
|
||
|
|
assert TensorProduct(JzKet(1, 1), JzKet(1, -1)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(1, 1), JzKet(1, -1)) )))
|
||
|
|
assert TensorProduct(JzKet(1, 0), JzKet(1, 1)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(1, 0), JzKet(1, 1)) )))
|
||
|
|
assert TensorProduct(JzKet(1, 0), JzKet(1, 0)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(1, 0), JzKet(1, 0)) )))
|
||
|
|
assert TensorProduct(JzKet(1, 0), JzKet(1, -1)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(1, 0), JzKet(1, -1)) )))
|
||
|
|
assert TensorProduct(JzKet(1, -1), JzKet(1, 1)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(1, -1), JzKet(1, 1)) )))
|
||
|
|
assert TensorProduct(JzKet(1, -1), JzKet(1, 0)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(1, -1), JzKet(1, 0)) )))
|
||
|
|
assert TensorProduct(JzKet(1, -1), JzKet(1, -1)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(1, -1), JzKet(1, -1)) )))
|
||
|
|
|
||
|
|
|
||
|
|
def test_uncouple_3_coupled_states():
|
||
|
|
# Default coupling
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S(
|
||
|
|
1)/2, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S(
|
||
|
|
1)/2, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S(
|
||
|
|
1)/2, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.NegativeOne/
|
||
|
|
2), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
# j1=1/2, j2=1, j3=1/2
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
# Coupling j1+j3=j13, j13+j2=j
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
# j1=1/2, j2=1, j3=1/2
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
1)/2), JzKet(1, 1), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
1)/2), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
1)/2), JzKet(1, 0), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
1)/2), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
1)/2), JzKet(1, -1), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
1)/2), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
-1)/2), JzKet(1, 1), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
-1)/2), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
-1)/2), JzKet(1, 0), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
-1)/2), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S(
|
||
|
|
-1)/2), JzKet(1, -1), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.NegativeOne/
|
||
|
|
2), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) )))
|
||
|
|
|
||
|
|
|
||
|
|
@slow
|
||
|
|
def test_uncouple_4_coupled_states():
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2, j4=1/2
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S(
|
||
|
|
1)/2, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S(
|
||
|
|
1)/2, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S(
|
||
|
|
1)/2, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S(
|
||
|
|
1)/2, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S(
|
||
|
|
1)/2, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S(
|
||
|
|
1)/2, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
# j1=1/2, j2=1/2, j3=1, j4=1/2
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half),
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half),
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)),
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)),
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) )))
|
||
|
|
# Couple j1+j3=j13, j2+j4=j24, j13+j24=j
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2, j4=1/2
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
# j1=1/2, j2=1/2, j3=1, j4=1/2
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, S.Half)), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
assert TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))) == \
|
||
|
|
expand(uncouple(couple( TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (2, 4), (1, 2)) )))
|
||
|
|
|
||
|
|
|
||
|
|
def test_uncouple_2_coupled_states_numerical():
|
||
|
|
# j1=1/2, j2=1/2
|
||
|
|
assert uncouple(JzKetCoupled(0, 0, (S.Half, S.Half))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))/2 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, 1, (S.Half, S.Half))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))
|
||
|
|
assert uncouple(JzKetCoupled(1, 0, (S.Half, S.Half))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, -1, (S.Half, S.Half))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))
|
||
|
|
# j1=1, j2=1/2
|
||
|
|
assert uncouple(JzKetCoupled(S.Half, S.Half, (1, S.Half))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(S.Half, S.Half))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, 1), JzKet(S.Half, Rational(-1, 2)))/3
|
||
|
|
assert uncouple(JzKetCoupled(S.Half, Rational(-1, 2), (1, S.Half))) == \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(S.Half, Rational(-1, 2)))/3 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, -1), JzKet(S.Half, S.Half))/3
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(3, 2), (1, S.Half))) == \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(S.Half, S.Half))
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), S.Half, (1, S.Half))) == \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(S.Half, Rational(-1, 2)))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, 0), JzKet(S.Half, S.Half))/3
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(-1, 2), (1, S.Half))) == \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, 0), JzKet(S.Half, Rational(-1, 2)))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(S.Half, S.Half))/3
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(-3, 2), (1, S.Half))) == \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(S.Half, Rational(-1, 2)))
|
||
|
|
# j1=1, j2=1
|
||
|
|
assert uncouple(JzKetCoupled(0, 0, (1, 1))) == \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(1, -1))/3 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(1, 1))/3
|
||
|
|
assert uncouple(JzKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, 1), JzKet(1, 0))/2 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, 0), JzKet(1, 1))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, 0, (1, 1))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, 1), JzKet(1, -1))/2 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, -1), JzKet(1, 1))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, -1, (1, 1))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, 0), JzKet(1, -1))/2 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, -1), JzKet(1, 0))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, 2, (1, 1))) == \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, 1))
|
||
|
|
assert uncouple(JzKetCoupled(2, 1, (1, 1))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, 1), JzKet(1, 0))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, 0), JzKet(1, 1))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, 0, (1, 1))) == \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, 1), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, 0), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, -1), JzKet(1, 1))/6
|
||
|
|
assert uncouple(JzKetCoupled(2, -1, (1, 1))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, 0), JzKet(1, -1))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, -1), JzKet(1, 0))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, -2, (1, 1))) == \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(1, -1))
|
||
|
|
|
||
|
|
|
||
|
|
def test_uncouple_3_coupled_states_numerical():
|
||
|
|
# Default coupling
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half))) == \
|
||
|
|
TensorProduct(JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half))) == \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))/3
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half))) == \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))/3
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half))) == \
|
||
|
|
TensorProduct(JzKet(
|
||
|
|
S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))
|
||
|
|
# j1=1/2, j2=1/2, j3=1
|
||
|
|
assert uncouple(JzKetCoupled(2, 2, (S.Half, S.Half, 1))) == \
|
||
|
|
TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1))
|
||
|
|
assert uncouple(JzKetCoupled(2, 1, (S.Half, S.Half, 1))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1))/2 + \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, 0, (S.Half, S.Half, 1))) == \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1))/6
|
||
|
|
assert uncouple(JzKetCoupled(2, -1, (S.Half, S.Half, 1))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))/2 + \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))/2 + \
|
||
|
|
TensorProduct(
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, -2, (S.Half, S.Half, 1))) == \
|
||
|
|
TensorProduct(
|
||
|
|
JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))
|
||
|
|
assert uncouple(JzKetCoupled(1, 1, (S.Half, S.Half, 1))) == \
|
||
|
|
-TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1))/2 - \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, 0, (S.Half, S.Half, 1))) == \
|
||
|
|
-sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, -1, (S.Half, S.Half, 1))) == \
|
||
|
|
-sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))/2 + \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1))/2 + \
|
||
|
|
TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))/2
|
||
|
|
# j1=1/2, j2=1, j3=1
|
||
|
|
assert uncouple(JzKetCoupled(Rational(5, 2), Rational(5, 2), (S.Half, 1, 1))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 1))
|
||
|
|
assert uncouple(JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, 1, 1))) == \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/5 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/5 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1),
|
||
|
|
JzKet(1, 0))/5
|
||
|
|
assert uncouple(JzKetCoupled(Rational(5, 2), S.Half, (S.Half, 1, 1))) == \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/5 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(10)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/10
|
||
|
|
assert uncouple(JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1))) == \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/10 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0),
|
||
|
|
JzKet(1, -1))/5
|
||
|
|
assert uncouple(JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, 1, 1))) == \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/5 + \
|
||
|
|
sqrt(5)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, -1))/5
|
||
|
|
assert uncouple(JzKetCoupled(Rational(5, 2), Rational(-5, 2), (S.Half, 1, 1))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, -1))
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1))) == \
|
||
|
|
-sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/15 - \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1),
|
||
|
|
JzKet(1, 0))/5
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1))) == \
|
||
|
|
-4*sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/15 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/15 - \
|
||
|
|
2*sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/15 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1),
|
||
|
|
JzKet(1, -1))/5
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1))) == \
|
||
|
|
-sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/5 - \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
2*sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/15 - \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/15 + \
|
||
|
|
4*sqrt(5)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/15
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1))) == \
|
||
|
|
-sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/5 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, -1))/15
|
||
|
|
assert uncouple(JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/3 - \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/6 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1),
|
||
|
|
JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/2 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/6 - \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/3 + \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/3
|
||
|
|
# j1=1, j2=1, j3=1
|
||
|
|
assert uncouple(JzKetCoupled(3, 3, (1, 1, 1))) == \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, 1))
|
||
|
|
assert uncouple(JzKetCoupled(3, 2, (1, 1, 1))) == \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, 0))/3
|
||
|
|
assert uncouple(JzKetCoupled(3, 1, (1, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 1))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 1))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 1))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, -1))/15
|
||
|
|
assert uncouple(JzKetCoupled(3, 0, (1, 1, 1))) == \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, -1))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, -1))/10
|
||
|
|
assert uncouple(JzKetCoupled(3, -1, (1, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 1))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, -1))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 0))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, -1))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, -1))/15
|
||
|
|
assert uncouple(JzKetCoupled(3, -2, (1, 1, 1))) == \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, -1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, -1))/3
|
||
|
|
assert uncouple(JzKetCoupled(3, -3, (1, 1, 1))) == \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, -1))
|
||
|
|
assert uncouple(JzKetCoupled(2, 2, (1, 1, 1))) == \
|
||
|
|
-sqrt(6)*TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 1))/6 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, 0))/3
|
||
|
|
assert uncouple(JzKetCoupled(2, 1, (1, 1, 1))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 1))/6 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 0))/6 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 0))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, -1))/3
|
||
|
|
assert uncouple(JzKetCoupled(2, 0, (1, 1, 1))) == \
|
||
|
|
-TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 1))/2 - \
|
||
|
|
TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 1))/2 + \
|
||
|
|
TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, -1))/2 + \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, -1, (1, 1, 1))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 1))/3 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 0))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, -1))/6 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 0))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, -1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, -1))/6
|
||
|
|
assert uncouple(JzKetCoupled(2, -2, (1, 1, 1))) == \
|
||
|
|
-sqrt(6)*TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, -1))/6
|
||
|
|
assert uncouple(JzKetCoupled(1, 1, (1, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 1))/30 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 1))/15 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 1))/30 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, -1))/5
|
||
|
|
assert uncouple(JzKetCoupled(1, 0, (1, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 1))/10 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 1))/10 - \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, -1))/10 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, -1))/10
|
||
|
|
assert uncouple(JzKetCoupled(1, -1, (1, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 1))/5 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, -1))/30 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, -1))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, -1))/30
|
||
|
|
# Defined j13
|
||
|
|
# j1=1/2, j2=1/2, j3=1, j13=1/2
|
||
|
|
assert uncouple(JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )) == \
|
||
|
|
-sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0))/3
|
||
|
|
assert uncouple(JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))/3 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1))/3
|
||
|
|
assert uncouple(JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))/3
|
||
|
|
# j1=1/2, j2=1, j3=1, j13=1/2
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))))) == \
|
||
|
|
-sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1),
|
||
|
|
JzKet(1, 0))/3
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))))) == \
|
||
|
|
-2*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/3 - \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1),
|
||
|
|
JzKet(1, -1))/3
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))))) == \
|
||
|
|
-sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/3 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/3 + \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/3 + \
|
||
|
|
2*TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/3
|
||
|
|
assert uncouple(JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(
|
||
|
|
JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, -1))/3
|
||
|
|
# j1=1, j2=1, j3=1, j13=1
|
||
|
|
assert uncouple(JzKetCoupled(2, 2, (1, 1, 1), ((1, 3, 1), (1, 2, 2)))) == \
|
||
|
|
-sqrt(2)*TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 1))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, 0))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)))) == \
|
||
|
|
-TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 1))/2 - \
|
||
|
|
TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 1))/2 + \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 0))/2 + \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 2)))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 1))/3 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 0))/6 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 0))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, -1))/3
|
||
|
|
assert uncouple(JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)))) == \
|
||
|
|
-TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 1))/2 - \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 0))/2 + \
|
||
|
|
TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, -1))/2 + \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, -2, (1, 1, 1), ((1, 3, 1), (1, 2, 2)))) == \
|
||
|
|
-sqrt(2)*TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 0))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)))) == \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 1))/2 - \
|
||
|
|
TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 1))/2 + \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 0))/2 - \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 1)))) == \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 0))/2 - \
|
||
|
|
TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 1))/2 - \
|
||
|
|
TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, -1))/2 + \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 0))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)))) == \
|
||
|
|
-TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 1))/2 + \
|
||
|
|
TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 0))/2 - \
|
||
|
|
TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, -1))/2 + \
|
||
|
|
TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, -1))/2
|
||
|
|
|
||
|
|
|
||
|
|
def test_uncouple_4_coupled_states_numerical():
|
||
|
|
# j1=1/2, j2=1/2, j3=1, j4=1, default coupling
|
||
|
|
assert uncouple(JzKetCoupled(3, 3, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
TensorProduct(JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 1))
|
||
|
|
assert uncouple(JzKetCoupled(3, 2, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/3
|
||
|
|
assert uncouple(JzKetCoupled(3, 1, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, 1), JzKet(1, -1))/15
|
||
|
|
assert uncouple(JzKetCoupled(3, 0, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/10 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, 0), JzKet(1, -1))/10
|
||
|
|
assert uncouple(JzKetCoupled(3, -1, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, -1), JzKet(1, -1))/15
|
||
|
|
assert uncouple(JzKetCoupled(3, -2, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
Rational(-1, 2)), JzKet(1, -1), JzKet(1, -1))/6
|
||
|
|
assert uncouple(JzKetCoupled(3, -3, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, -S(
|
||
|
|
1)/2), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, -1))
|
||
|
|
assert uncouple(JzKetCoupled(2, 2, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 1))/6 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/6 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/3
|
||
|
|
assert uncouple(JzKetCoupled(2, 1, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/6 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/12 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/12 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/3
|
||
|
|
assert uncouple(JzKetCoupled(2, 0, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
-TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/2 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/4 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/4 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/4 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/4 + \
|
||
|
|
TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, -1, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/3 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/6 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/12 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/6 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/12 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, -1), JzKet(1, -1))/6
|
||
|
|
assert uncouple(JzKetCoupled(2, -2, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
-sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
Rational(-1, 2)), JzKet(1, -1), JzKet(1, -1))/6
|
||
|
|
assert uncouple(JzKetCoupled(1, 1, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/30 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/30 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/20 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/30 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/20 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/30 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/5
|
||
|
|
assert uncouple(JzKetCoupled(1, 0, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/10 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/20 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/20 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/20 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/20 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, 0), JzKet(1, -1))/10
|
||
|
|
assert uncouple(JzKetCoupled(1, -1, (S.Half, S.Half, 1, 1))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/5 - \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/30 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/20 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/30 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/20 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/30 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, -1), JzKet(1, -1))/30
|
||
|
|
# j1=1/2, j2=1/2, j3=1, j4=1, j12=1, j34=1
|
||
|
|
assert uncouple(JzKetCoupled(2, 2, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 1), (1, 3, 2)))) == \
|
||
|
|
-sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, 1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 1), (1, 3, 2)))) == \
|
||
|
|
-sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/4 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/4 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/4 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/4 - \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/2 + \
|
||
|
|
TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, 0, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 1), (1, 3, 2)))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/6 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/6 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/6 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/6
|
||
|
|
assert uncouple(JzKetCoupled(2, -1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 1), (1, 3, 2)))) == \
|
||
|
|
-TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/2 + \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/2 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/4 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/4 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/4 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/4
|
||
|
|
assert uncouple(JzKetCoupled(2, -2, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 1), (1, 3, 2)))) == \
|
||
|
|
-sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/2 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half,
|
||
|
|
Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, 1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 1), (1, 3, 1)))) == \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/4 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/4 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/4 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/4 - \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/2 + \
|
||
|
|
TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, 0, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 1), (1, 3, 1)))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/2 - \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/2 - \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/2 + \
|
||
|
|
TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(1, -1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 1), (1, 3, 1)))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/2 - \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/2 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/4 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/4 - \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/4 + \
|
||
|
|
sqrt(2)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/4
|
||
|
|
# j1=1/2, j2=1/2, j3=1, j4=1, j12=1, j34=2
|
||
|
|
assert uncouple(JzKetCoupled(3, 3, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 3)))) == \
|
||
|
|
TensorProduct(JzKet(
|
||
|
|
S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 1))
|
||
|
|
assert uncouple(JzKetCoupled(3, 2, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 3)))) == \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/3
|
||
|
|
assert uncouple(JzKetCoupled(3, 1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 3)))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, 1), JzKet(1, -1))/15
|
||
|
|
assert uncouple(JzKetCoupled(3, 0, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 3)))) == \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/10 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/5 + \
|
||
|
|
sqrt(5)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(10)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, 0), JzKet(1, -1))/10
|
||
|
|
assert uncouple(JzKetCoupled(3, -1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 3)))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/15 + \
|
||
|
|
2*sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, -1), JzKet(1, -1))/15
|
||
|
|
assert uncouple(JzKetCoupled(3, -2, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 3)))) == \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
Rational(-1, 2)), JzKet(1, -1), JzKet(1, -1))/6
|
||
|
|
assert uncouple(JzKetCoupled(3, -3, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 3)))) == \
|
||
|
|
TensorProduct(JzKet(S.Half, -S(
|
||
|
|
1)/2), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, -1))
|
||
|
|
assert uncouple(JzKetCoupled(2, 2, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 2)))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 1))/3 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/3 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/6
|
||
|
|
assert uncouple(JzKetCoupled(2, 1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 2)))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/3 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/12 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/12 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/12 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/12 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/6
|
||
|
|
assert uncouple(JzKetCoupled(2, 0, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 2)))) == \
|
||
|
|
-TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/2 - \
|
||
|
|
TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/2 + \
|
||
|
|
TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/2 + \
|
||
|
|
TensorProduct(JzKet(S(
|
||
|
|
1)/2, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/2
|
||
|
|
assert uncouple(JzKetCoupled(2, -1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 2)))) == \
|
||
|
|
-sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/6 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/3 - \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/12 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/12 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/12 + \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/12 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, -1), JzKet(1, -1))/3
|
||
|
|
assert uncouple(JzKetCoupled(2, -2, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 2)))) == \
|
||
|
|
-sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/6 - \
|
||
|
|
sqrt(6)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/6 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, -1))/3 + \
|
||
|
|
sqrt(3)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
Rational(-1, 2)), JzKet(1, -1), JzKet(1, -1))/3
|
||
|
|
assert uncouple(JzKetCoupled(1, 1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 1)))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))/5 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))/20 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))/20 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/20 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/20 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/30 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, 1), JzKet(1, -1))/30
|
||
|
|
assert uncouple(JzKetCoupled(1, 0, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 1)))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))/10 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))/10 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))/30 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))/15 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))/30 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/30 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/15 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/30 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/10 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, 0), JzKet(1, -1))/10
|
||
|
|
assert uncouple(JzKetCoupled(1, -1, (S.Half, S.Half, 1, 1), ((1, 2, 1), (3, 4, 2), (1, 3, 1)))) == \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))/30 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))/15 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))/30 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))/20 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))/20 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))/20 - \
|
||
|
|
sqrt(30)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))/20 + \
|
||
|
|
sqrt(15)*TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half,
|
||
|
|
S.Half), JzKet(1, -1), JzKet(1, -1))/5
|
||
|
|
|
||
|
|
|
||
|
|
def test_uncouple_symbolic():
|
||
|
|
assert uncouple(JzKetCoupled(j, m, (j1, j2) )) == \
|
||
|
|
Sum(CG(j1, m1, j2, m2, j, m) *
|
||
|
|
TensorProduct(JzKet(j1, m1), JzKet(j2, m2)),
|
||
|
|
(m1, -j1, j1), (m2, -j2, j2))
|
||
|
|
assert uncouple(JzKetCoupled(j, m, (j1, j2, j3) )) == \
|
||
|
|
Sum(CG(j1, m1, j2, m2, j1 + j2, m1 + m2) * CG(j1 + j2, m1 + m2, j3, m3, j, m) *
|
||
|
|
TensorProduct(JzKet(j1, m1), JzKet(j2, m2), JzKet(j3, m3)),
|
||
|
|
(m1, -j1, j1), (m2, -j2, j2), (m3, -j3, j3))
|
||
|
|
assert uncouple(JzKetCoupled(j, m, (j1, j2, j3), ((1, 3, j13), (1, 2, j)) )) == \
|
||
|
|
Sum(CG(j1, m1, j3, m3, j13, m1 + m3) * CG(j13, m1 + m3, j2, m2, j, m) *
|
||
|
|
TensorProduct(JzKet(j1, m1), JzKet(j2, m2), JzKet(j3, m3)),
|
||
|
|
(m1, -j1, j1), (m2, -j2, j2), (m3, -j3, j3))
|
||
|
|
assert uncouple(JzKetCoupled(j, m, (j1, j2, j3, j4) )) == \
|
||
|
|
Sum(CG(j1, m1, j2, m2, j1 + j2, m1 + m2) * CG(j1 + j2, m1 + m2, j3, m3, j1 + j2 + j3, m1 + m2 + m3) * CG(j1 + j2 + j3, m1 + m2 + m3, j4, m4, j, m) *
|
||
|
|
TensorProduct(
|
||
|
|
JzKet(j1, m1), JzKet(j2, m2), JzKet(j3, m3), JzKet(j4, m4)),
|
||
|
|
(m1, -j1, j1), (m2, -j2, j2), (m3, -j3, j3), (m4, -j4, j4))
|
||
|
|
assert uncouple(JzKetCoupled(j, m, (j1, j2, j3, j4), ((1, 3, j13), (2, 4, j24), (1, 2, j)) )) == \
|
||
|
|
Sum(CG(j1, m1, j3, m3, j13, m1 + m3) * CG(j2, m2, j4, m4, j24, m2 + m4) * CG(j13, m1 + m3, j24, m2 + m4, j, m) *
|
||
|
|
TensorProduct(
|
||
|
|
JzKet(j1, m1), JzKet(j2, m2), JzKet(j3, m3), JzKet(j4, m4)),
|
||
|
|
(m1, -j1, j1), (m2, -j2, j2), (m3, -j3, j3), (m4, -j4, j4))
|
||
|
|
|
||
|
|
|
||
|
|
def test_couple_2_states():
|
||
|
|
# j1=1/2, j2=1/2
|
||
|
|
assert JzKetCoupled(0, 0, (S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(0, 0, (S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(1, 1, (S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 1, (S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(1, 0, (S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 0, (S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(1, -1, (S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, -1, (S.Half, S.Half)) )))
|
||
|
|
# j1=1, j2=1/2
|
||
|
|
assert JzKetCoupled(S.Half, S.Half, (1, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(S.Half, S.Half, (1, S.Half)) )))
|
||
|
|
assert JzKetCoupled(S.Half, Rational(-1, 2), (1, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(S.Half, Rational(-1, 2), (1, S.Half)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(3, 2), (1, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), Rational(3, 2), (1, S.Half)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), S.Half, (1, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), S.Half, (1, S.Half)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-1, 2), (1, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), Rational(-1, 2), (1, S.Half)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-3, 2), (1, S.Half)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), Rational(-3, 2), (1, S.Half)) )))
|
||
|
|
# j1=1, j2=1
|
||
|
|
assert JzKetCoupled(0, 0, (1, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(0, 0, (1, 1)) )))
|
||
|
|
assert JzKetCoupled(1, 1, (1, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 1, (1, 1)) )))
|
||
|
|
assert JzKetCoupled(1, 0, (1, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 0, (1, 1)) )))
|
||
|
|
assert JzKetCoupled(1, -1, (1, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, -1, (1, 1)) )))
|
||
|
|
assert JzKetCoupled(2, 2, (1, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 2, (1, 1)) )))
|
||
|
|
assert JzKetCoupled(2, 1, (1, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 1, (1, 1)) )))
|
||
|
|
assert JzKetCoupled(2, 0, (1, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 0, (1, 1)) )))
|
||
|
|
assert JzKetCoupled(2, -1, (1, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, -1, (1, 1)) )))
|
||
|
|
assert JzKetCoupled(2, -2, (1, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, -2, (1, 1)) )))
|
||
|
|
# j1=1/2, j2=3/2
|
||
|
|
assert JzKetCoupled(1, 1, (S.Half, Rational(3, 2))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 1, (S.Half, Rational(3, 2))) )))
|
||
|
|
assert JzKetCoupled(1, 0, (S.Half, Rational(3, 2))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 0, (S.Half, Rational(3, 2))) )))
|
||
|
|
assert JzKetCoupled(1, -1, (S.Half, Rational(3, 2))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, -1, (S.Half, Rational(3, 2))) )))
|
||
|
|
assert JzKetCoupled(2, 2, (S.Half, Rational(3, 2))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 2, (S.Half, Rational(3, 2))) )))
|
||
|
|
assert JzKetCoupled(2, 1, (S.Half, Rational(3, 2))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 1, (S.Half, Rational(3, 2))) )))
|
||
|
|
assert JzKetCoupled(2, 0, (S.Half, Rational(3, 2))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 0, (S.Half, Rational(3, 2))) )))
|
||
|
|
assert JzKetCoupled(2, -1, (S.Half, Rational(3, 2))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, -1, (S.Half, Rational(3, 2))) )))
|
||
|
|
assert JzKetCoupled(2, -2, (S.Half, Rational(3, 2))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, -2, (S.Half, Rational(3, 2))) )))
|
||
|
|
|
||
|
|
|
||
|
|
def test_couple_3_states():
|
||
|
|
# Default coupling
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2
|
||
|
|
assert JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half)) )))
|
||
|
|
# j1=1/2, j2=1/2, j3=1
|
||
|
|
assert JzKetCoupled(0, 0, (S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(0, 0, (S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(1, 1, (S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 1, (S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(1, 0, (S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 0, (S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(1, -1, (S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, -1, (S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(2, 2, (S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 2, (S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(2, 1, (S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 1, (S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(2, 0, (S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 0, (S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(2, -1, (S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, -1, (S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(2, -2, (S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, -2, (S.Half, S.Half, 1)) )))
|
||
|
|
# Couple j1+j3=j13, j13+j2=j
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2, j13=0
|
||
|
|
assert JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 3, 0), (1, 2, S.Half))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(S.Half, S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half), ((1, 3, 0), (1, 2, S.Half))) ), ((1, 3), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 3, 0), (1, 2, S.Half))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half), ((1, 3, 0), (1, 2, S.Half))) ), ((1, 3), (1, 2)) ))
|
||
|
|
# j1=1, j2=1/2, j3=1, j13=1
|
||
|
|
assert JzKetCoupled(S.Half, S.Half, (1, S.Half, 1), ((1, 3, 1), (1, 2, S.Half))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(S.Half, S.Half, (
|
||
|
|
1, S.Half, 1), ((1, 3, 1), (1, 2, S.Half))) ), ((1, 3), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(S.Half, Rational(-1, 2), (1, S.Half, 1), ((1, 3, 1), (1, 2, S.Half))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(S.Half, Rational(-1, 2), (
|
||
|
|
1, S.Half, 1), ((1, 3, 1), (1, 2, S.Half))) ), ((1, 3), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(3, 2), (1, S.Half, 1), ((1, 3, 1), (1, 2, Rational(3, 2)))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), Rational(3, 2), (
|
||
|
|
1, S.Half, 1), ((1, 3, 1), (1, 2, Rational(3, 2)))) ), ((1, 3), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), S.Half, (1, S.Half, 1), ((1, 3, 1), (1, 2, Rational(3, 2)))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), S.Half, (
|
||
|
|
1, S.Half, 1), ((1, 3, 1), (1, 2, Rational(3, 2)))) ), ((1, 3), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-1, 2), (1, S.Half, 1), ((1, 3, 1), (1, 2, Rational(3, 2)))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), Rational(-1, 2), (
|
||
|
|
1, S.Half, 1), ((1, 3, 1), (1, 2, Rational(3, 2)))) ), ((1, 3), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-3, 2), (1, S.Half, 1), ((1, 3, 1), (1, 2, Rational(3, 2)))) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), Rational(-3, 2), (
|
||
|
|
1, S.Half, 1), ((1, 3, 1), (1, 2, Rational(3, 2)))) ), ((1, 3), (1, 2)) ))
|
||
|
|
|
||
|
|
|
||
|
|
def test_couple_4_states():
|
||
|
|
# Default coupling
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2, j4=1/2
|
||
|
|
assert JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(
|
||
|
|
uncouple( JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(
|
||
|
|
uncouple( JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(2, 2, (S.Half, S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(
|
||
|
|
uncouple( JzKetCoupled(2, 2, (S.Half, S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(2, 1, (S.Half, S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(
|
||
|
|
uncouple( JzKetCoupled(2, 1, (S.Half, S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(2, 0, (S.Half, S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(
|
||
|
|
uncouple( JzKetCoupled(2, 0, (S.Half, S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(2, -1, (S.Half, S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S.Half, S.Half, S.Half)) )))
|
||
|
|
assert JzKetCoupled(2, -2, (S.Half, S.Half, S.Half, S.Half)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(2, -2, (S.Half, S.Half, S.Half, S.Half)) )))
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2, j4=1
|
||
|
|
assert JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(5, 2), Rational(5, 2), (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(5, 2), Rational(5, 2), (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
assert JzKetCoupled(Rational(5, 2), Rational(-5, 2), (S.Half, S.Half, S.Half, 1)) == \
|
||
|
|
expand(couple(uncouple(
|
||
|
|
JzKetCoupled(Rational(5, 2), Rational(-5, 2), (S.Half, S.Half, S.Half, 1)) )))
|
||
|
|
# Coupling j1+j3=j13, j2+j4=j24, j13+j24=j
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2, j4=1/2, j13=1, j24=0
|
||
|
|
assert JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 3, 1), (2, 4, 0), (1, 2, 1)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 3, 1), (2, 4, 0), (1, 2, 1)) ) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 3, 1), (2, 4, 0), (1, 2, 1)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 3, 1), (2, 4, 0), (1, 2, 1)) ) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 3, 1), (2, 4, 0), (1, 2, 1)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 3, 1), (2, 4, 0), (1, 2, 1)) ) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2, j4=1, j13=1, j24=1/2
|
||
|
|
assert JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, S.Half)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, S.Half)) )), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, S.Half)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, S.Half)) ) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, Rational(3, 2))) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, Rational(3, 2))) ) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, Rational(3, 2))) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, Rational(3, 2))) ) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, Rational(3, 2))) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, Rational(3, 2))) ) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, Rational(3, 2))) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 3, 1), (2, 4, S.Half), (1, 2, Rational(3, 2))) ) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
# j1=1/2, j2=1, j3=1/2, j4=1, j13=0, j24=1
|
||
|
|
assert JzKetCoupled(1, 1, (S.Half, 1, S.Half, 1), ((1, 3, 0), (2, 4, 1), (1, 2, 1)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 1, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 0), (2, 4, 1), (1, 2, 1))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(1, 0, (S.Half, 1, S.Half, 1), ((1, 3, 0), (2, 4, 1), (1, 2, 1)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 0, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 0), (2, 4, 1), (1, 2, 1))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(1, -1, (S.Half, 1, S.Half, 1), ((1, 3, 0), (2, 4, 1), (1, 2, 1)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, -1, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 0), (2, 4, 1), (1, 2, 1))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
# j1=1/2, j2=1, j3=1/2, j4=1, j13=1, j24=1
|
||
|
|
assert JzKetCoupled(0, 0, (S.Half, 1, S.Half, 1), ((1, 3, 1), (2, 4, 1), (1, 2, 0)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(0, 0, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 1), (2, 4, 1), (1, 2, 0))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(1, 1, (S.Half, 1, S.Half, 1), ((1, 3, 1), (2, 4, 1), (1, 2, 1)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 1, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 1), (2, 4, 1), (1, 2, 1))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(1, 0, (S.Half, 1, S.Half, 1), ((1, 3, 1), (2, 4, 1), (1, 2, 1)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, 0, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 1), (2, 4, 1), (1, 2, 1))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(1, -1, (S.Half, 1, S.Half, 1), ((1, 3, 1), (2, 4, 1), (1, 2, 1)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(1, -1, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 1), (2, 4, 1), (1, 2, 1))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(2, 2, (S.Half, 1, S.Half, 1), ((1, 3, 1), (2, 4, 1), (1, 2, 2)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 2, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 1), (2, 4, 1), (1, 2, 2))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(2, 1, (S.Half, 1, S.Half, 1), ((1, 3, 1), (2, 4, 1), (1, 2, 2)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 1, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 1), (2, 4, 1), (1, 2, 2))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(2, 0, (S.Half, 1, S.Half, 1), ((1, 3, 1), (2, 4, 1), (1, 2, 2)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, 0, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 1), (2, 4, 1), (1, 2, 2))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(2, -1, (S.Half, 1, S.Half, 1), ((1, 3, 1), (2, 4, 1), (1, 2, 2)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, -1, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 1), (2, 4, 1), (1, 2, 2))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
assert JzKetCoupled(2, -2, (S.Half, 1, S.Half, 1), ((1, 3, 1), (2, 4, 1), (1, 2, 2)) ) == \
|
||
|
|
expand(couple(uncouple( JzKetCoupled(2, -2, (S.Half, 1, S.Half, 1), (
|
||
|
|
(1, 3, 1), (2, 4, 1), (1, 2, 2))) ), ((1, 3), (2, 4), (1, 2)) ))
|
||
|
|
|
||
|
|
|
||
|
|
def test_couple_2_states_numerical():
|
||
|
|
# j1=1/2, j2=1/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))) == \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half))
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(0, 0, (S(
|
||
|
|
1)/2, S.Half))/2 + sqrt(2)*JzKetCoupled(1, 0, (S.Half, S.Half))/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(0, 0, (S(
|
||
|
|
1)/2, S.Half))/2 + sqrt(2)*JzKetCoupled(1, 0, (S.Half, S.Half))/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
JzKetCoupled(1, -1, (S.Half, S.Half))
|
||
|
|
# j1=1, j2=1/2
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(S.Half, S.Half))) == \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(3, 2), (1, S.Half))
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (1, S.Half))/3 + sqrt(
|
||
|
|
3)*JzKetCoupled(Rational(3, 2), S.Half, (1, S.Half))/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(S.Half, S.Half))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(S.Half, S.Half, (1, S.Half))/3 + \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), S.Half, (1, S.Half))/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(S.Half, Rational(-1, 2), (1, S.Half))/3 + \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (1, S.Half))/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(S.Half, S.Half))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (1, S(
|
||
|
|
1)/2))/3 + sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (1, S.Half))/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-3, 2), (1, S.Half))
|
||
|
|
# j1=1, j2=1
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 1))) == \
|
||
|
|
JzKetCoupled(2, 2, (1, 1))
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 0))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(
|
||
|
|
1, 1, (1, 1))/2 + sqrt(2)*JzKetCoupled(2, 1, (1, 1))/2
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (1, 1))/3 + sqrt(2)*JzKetCoupled(
|
||
|
|
1, 0, (1, 1))/2 + sqrt(6)*JzKetCoupled(2, 0, (1, 1))/6
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 1))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(
|
||
|
|
1, 1, (1, 1))/2 + sqrt(2)*JzKetCoupled(2, 1, (1, 1))/2
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 0))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(
|
||
|
|
0, 0, (1, 1))/3 + sqrt(6)*JzKetCoupled(2, 0, (1, 1))/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, -1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(
|
||
|
|
1, -1, (1, 1))/2 + sqrt(2)*JzKetCoupled(2, -1, (1, 1))/2
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (1, 1))/3 - sqrt(2)*JzKetCoupled(
|
||
|
|
1, 0, (1, 1))/2 + sqrt(6)*JzKetCoupled(2, 0, (1, 1))/6
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 0))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(
|
||
|
|
1, -1, (1, 1))/2 + sqrt(2)*JzKetCoupled(2, -1, (1, 1))/2
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, -1))) == \
|
||
|
|
JzKetCoupled(2, -2, (1, 1))
|
||
|
|
# j1=3/2, j2=1/2
|
||
|
|
assert couple(TensorProduct(JzKet(Rational(3, 2), Rational(3, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
JzKetCoupled(2, 2, (Rational(3, 2), S.Half))
|
||
|
|
assert couple(TensorProduct(JzKet(Rational(3, 2), Rational(3, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(
|
||
|
|
1, 1, (Rational(3, 2), S.Half))/2 + JzKetCoupled(2, 1, (Rational(3, 2), S.Half))/2
|
||
|
|
assert couple(TensorProduct(JzKet(Rational(3, 2), S.Half), JzKet(S.Half, S.Half))) == \
|
||
|
|
-JzKetCoupled(1, 1, (S(
|
||
|
|
3)/2, S.Half))/2 + sqrt(3)*JzKetCoupled(2, 1, (Rational(3, 2), S.Half))/2
|
||
|
|
assert couple(TensorProduct(JzKet(Rational(3, 2), S.Half), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 0, (S(
|
||
|
|
3)/2, S.Half))/2 + sqrt(2)*JzKetCoupled(2, 0, (Rational(3, 2), S.Half))/2
|
||
|
|
assert couple(TensorProduct(JzKet(Rational(3, 2), Rational(-1, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, 0, (S(
|
||
|
|
3)/2, S.Half))/2 + sqrt(2)*JzKetCoupled(2, 0, (Rational(3, 2), S.Half))/2
|
||
|
|
assert couple(TensorProduct(JzKet(Rational(3, 2), Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
JzKetCoupled(1, -1, (S(
|
||
|
|
3)/2, S.Half))/2 + sqrt(3)*JzKetCoupled(2, -1, (Rational(3, 2), S.Half))/2
|
||
|
|
assert couple(TensorProduct(JzKet(Rational(3, 2), Rational(-3, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, -1, (Rational(3, 2), S.Half))/2 + \
|
||
|
|
JzKetCoupled(2, -1, (Rational(3, 2), S.Half))/2
|
||
|
|
assert couple(TensorProduct(JzKet(Rational(3, 2), Rational(-3, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
JzKetCoupled(2, -2, (Rational(3, 2), S.Half))
|
||
|
|
|
||
|
|
|
||
|
|
def test_couple_3_states_numerical():
|
||
|
|
# Default coupling
|
||
|
|
# j1=1/2,j2=1/2,j3=1/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))) == \
|
||
|
|
JzKetCoupled(Rational(3, 2), S(
|
||
|
|
3)/2, (S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2))) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 2, 1), (1, 3, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 2, 1), (1, 3, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.One
|
||
|
|
/2), ((1, 2, 1), (1, 3, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 2, 1), (1, 3, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.One
|
||
|
|
/2), ((1, 2, 1), (1, 3, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.One
|
||
|
|
/2), ((1, 2, 1), (1, 3, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
JzKetCoupled(Rational(3, 2), -S(
|
||
|
|
3)/2, (S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2))) )
|
||
|
|
# j1=S.Half, j2=S.Half, j3=1
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1))) == \
|
||
|
|
JzKetCoupled(2, 2, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(2)*JzKetCoupled(
|
||
|
|
2, 1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 0)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(
|
||
|
|
2, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 2, 0), (1, 3, 1)) )/2 - \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(0, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 0)) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 2, 0), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(
|
||
|
|
2, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 2, 0), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 2, 0), (1, 3, 1)) )/2 - \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(0, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 0)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 2, 0), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(
|
||
|
|
2, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 2, 0), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 0)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(
|
||
|
|
2, 0, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(2)*JzKetCoupled(
|
||
|
|
2, -1, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))) == \
|
||
|
|
JzKetCoupled(2, -2, (S.Half, S.Half, 1), ((1, 2, 1), (1, 3, 2)) )
|
||
|
|
# j1=S.Half, j2=1, j3=1
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 1))) == \
|
||
|
|
JzKetCoupled(
|
||
|
|
Rational(5, 2), Rational(5, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(5, 2))) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0))) == \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(S(
|
||
|
|
5)/2, Rational(3, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
2*sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(S(
|
||
|
|
5)/2, Rational(3, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0))) == \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(S(
|
||
|
|
5)/2, S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
4*sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1))) == \
|
||
|
|
-2*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/3 + \
|
||
|
|
2*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, -1))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(S(
|
||
|
|
5)/2, Rational(3, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/3 - \
|
||
|
|
2*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(S(
|
||
|
|
5)/2, S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
-2*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
4*sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(S(
|
||
|
|
5)/2, S.Half, (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0))) == \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 2, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, S.Half)) )/2 - \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0))) == \
|
||
|
|
-sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, 1, 1), ((1,
|
||
|
|
2, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, -1))) == \
|
||
|
|
JzKetCoupled(S(
|
||
|
|
5)/2, Rational(-5, 2), (S.Half, 1, 1), ((1, 2, Rational(3, 2)), (1, 3, Rational(5, 2))) )
|
||
|
|
# j1=1, j2=1, j3=1
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, 1))) == \
|
||
|
|
JzKetCoupled(3, 3, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, 0))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, 2, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/5 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/3 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, 2, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 0))) == \
|
||
|
|
JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/10 + \
|
||
|
|
JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, -1))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 0)) )/6 + \
|
||
|
|
JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/10 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/6 + \
|
||
|
|
JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 0), (1, 3, 1)) )/3 - \
|
||
|
|
JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/30 + \
|
||
|
|
JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 0))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 0)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 0), (1, 3, 1)) )/3 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/15 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/3 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, -1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 0), (1, 3, 1)) )/3 + \
|
||
|
|
JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/30 + \
|
||
|
|
JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 1))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, 2, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 0))) == \
|
||
|
|
-JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/10 - \
|
||
|
|
JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 0)) )/6 - \
|
||
|
|
JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/10 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/6 + \
|
||
|
|
JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 1))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 0), (1, 3, 1)) )/3 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/15 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/3 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 0))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 0), (1, 3, 1)) )/3 - \
|
||
|
|
2*sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, -1))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 0), (1, 3, 1)) )/3 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/15 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/3 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 1))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 0)) )/6 - \
|
||
|
|
JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/10 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/6 - \
|
||
|
|
JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 0))) == \
|
||
|
|
-JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/10 + \
|
||
|
|
JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, -1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, -2, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 0), (1, 3, 1)) )/3 + \
|
||
|
|
JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/30 - \
|
||
|
|
JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 0))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 0)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 0), (1, 3, 1)) )/3 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/15 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/3 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 0), (1, 3, 1)) )/3 - \
|
||
|
|
JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/30 - \
|
||
|
|
JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 1))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 0)) )/6 + \
|
||
|
|
JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/10 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/6 - \
|
||
|
|
JzKetCoupled(2, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 0))) == \
|
||
|
|
JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 1), (1, 3, 1)) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/10 - \
|
||
|
|
JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, -1))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 2, 1), (1, 3, 2)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, -2, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 1))) == \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 1)) )/5 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/3 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 0))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 2, 2), (1, 3, 2)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, -2, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, -1))) == \
|
||
|
|
JzKetCoupled(3, -3, (1, 1, 1), ((1, 2, 2), (1, 3, 3)) )
|
||
|
|
# j1=S.Half, j2=S.Half, j3=Rational(3, 2)
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(3, 2)))) == \
|
||
|
|
JzKetCoupled(Rational(5, 2), S(
|
||
|
|
5)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), S.Half))) == \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S.Half, S(3)
|
||
|
|
/2), ((1, 2, 1), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(-1, 2)))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, S.Half)) )/6 + \
|
||
|
|
2*sqrt(30)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(-3, 2)))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, S.Half)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(3, 2)))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 0), (1, 3, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S.Half, S(3)/
|
||
|
|
2), ((1, 2, 1), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), S.Half))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 0), (1, 3, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/30 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(-1, 2)))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 0), (1, 3, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/30 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(-3, 2)))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 0), (1, 3, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S.Half, S(3)
|
||
|
|
/2), ((1, 2, 1), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(3, 2)))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 0), (1, 3, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S.Half, S(3)/
|
||
|
|
2), ((1, 2, 1), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), S.Half))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 0), (1, 3, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/30 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(-1, 2)))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 0), (1, 3, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/30 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(-3, 2)))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 0), (1, 3, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S.Half, S(3)
|
||
|
|
/2), ((1, 2, 1), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(3, 2)))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, S.Half)) )/2 - \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), S.Half))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, S.Half)) )/6 - \
|
||
|
|
2*sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(-1, 2)))) == \
|
||
|
|
-sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S.Half, S(
|
||
|
|
3)/2), ((1, 2, 1), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(-3, 2)))) == \
|
||
|
|
JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
5)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 2, 1), (1, 3, Rational(5, 2))) )
|
||
|
|
# Couple j1 to j3
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(Rational(3, 2), S(
|
||
|
|
3)/2, (S.Half, S.Half, S.Half), ((1, 3, 1), (1, 2, Rational(3, 2))) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 3, 0), (1, 2, S.Half)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 3, 1), (1, 2, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 3, 1), (1, 2, S.Half)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 3, 0), (1, 2, S.Half)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 3, 1), (1, 2, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.One
|
||
|
|
/2), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 3, 0), (1, 2, S.Half)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half), ((1, 3, 1), (1, 2, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 3, 1), (1, 2, S.Half)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.One
|
||
|
|
/2), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 3, 0), (1, 2, S.Half)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half), ((1, 3, 1), (1, 2, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.One
|
||
|
|
/2), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(Rational(3, 2), -S(
|
||
|
|
3)/2, (S.Half, S.Half, S.Half), ((1, 3, 1), (1, 2, Rational(3, 2))) )
|
||
|
|
# j1=1/2, j2=1/2, j3=1
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(2, 2, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )/3 - \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(
|
||
|
|
2, 1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 0)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )/3 - \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(
|
||
|
|
2, 0, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(0, 0, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 0)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(
|
||
|
|
2, 0, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/6 + \
|
||
|
|
JzKetCoupled(
|
||
|
|
2, -1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )/3 - \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/6 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(0, 0, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 0)) )/6 - \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )/6 - \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(
|
||
|
|
2, 0, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/2 + \
|
||
|
|
JzKetCoupled(
|
||
|
|
2, -1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 0)) )/3 - \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )/3 + \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(
|
||
|
|
2, 0, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 3, S.Half), (1, 2, 1)) )/3 + \
|
||
|
|
sqrt(6)*JzKetCoupled(1, -1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 1)) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(
|
||
|
|
2, -1, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(2, -2, (S.Half, S.Half, 1), ((1, 3, Rational(3, 2)), (1, 2, 2)) )
|
||
|
|
# j 1=1/2, j 2=1, j 3=1
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(
|
||
|
|
Rational(5, 2), Rational(5, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(5, 2))) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 - \
|
||
|
|
2*sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(S(
|
||
|
|
5)/2, Rational(3, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-2*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 - \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(S(
|
||
|
|
5)/2, Rational(3, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(S(
|
||
|
|
5)/2, S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, 0), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/3 + \
|
||
|
|
2*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 + \
|
||
|
|
4*sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(1, -1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(S(
|
||
|
|
5)/2, Rational(3, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 - \
|
||
|
|
4*sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(S(
|
||
|
|
5)/2, S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/2 - \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/3 - \
|
||
|
|
2*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(S(
|
||
|
|
5)/2, S.Half, (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-2*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 + \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 3, S.Half), (1, 2, Rational(3, 2))) )/3 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, 1, 1), ((1,
|
||
|
|
3, Rational(3, 2)), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(S(
|
||
|
|
5)/2, Rational(-5, 2), (S.Half, 1, 1), ((1, 3, Rational(3, 2)), (1, 2, Rational(5, 2))) )
|
||
|
|
# j1=1, 1, 1
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(3, 3, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, 2, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 0), (1, 2, 1)) )/3 - \
|
||
|
|
JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/30 + \
|
||
|
|
JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, 2, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/10 + \
|
||
|
|
JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, 0), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 0)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 0), (1, 2, 1)) )/3 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/15 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/3 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/5 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/3 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 0)) )/6 + \
|
||
|
|
JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/10 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/6 + \
|
||
|
|
JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, 1), JzKet(1, -1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 0), (1, 2, 1)) )/3 + \
|
||
|
|
JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/30 + \
|
||
|
|
JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 2, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, 2, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 0), (1, 2, 1)) )/3 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/15 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/3 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 0)) )/6 - \
|
||
|
|
JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/10 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/6 - \
|
||
|
|
JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/10 - \
|
||
|
|
JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 0), (1, 2, 1)) )/3 - \
|
||
|
|
2*sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, 0), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/10 + \
|
||
|
|
JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 0)) )/6 - \
|
||
|
|
JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/10 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/6 + \
|
||
|
|
JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 0), (1, 2, 1)) )/3 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/15 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/3 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, 0), JzKet(1, -1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, -2, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 0), (1, 2, 1)) )/3 + \
|
||
|
|
JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/30 - \
|
||
|
|
JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, 1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 0)) )/6 + \
|
||
|
|
JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/10 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/6 - \
|
||
|
|
JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/5 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/3 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(0, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 0)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 0), (1, 2, 1)) )/3 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/15 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, 0, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/3 + \
|
||
|
|
sqrt(10)*JzKetCoupled(3, 0, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/10 - \
|
||
|
|
JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, 0), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, -2, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 0), (1, 2, 1)) )/3 - \
|
||
|
|
JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 1)) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(1, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 1)) )/30 - \
|
||
|
|
JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(2, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
sqrt(15)*JzKetCoupled(3, -1, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/15
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, 0)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 3, 1), (1, 2, 2)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, -2, (1, 1, 1), ((1, 3, 2), (1, 2, 2)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(3, -2, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )/3
|
||
|
|
assert couple(TensorProduct(JzKet(1, -1), JzKet(1, -1), JzKet(1, -1)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(3, -3, (1, 1, 1), ((1, 3, 2), (1, 2, 3)) )
|
||
|
|
# j1=1/2, j2=1/2, j3=3/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(3, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(Rational(5, 2), S(
|
||
|
|
5)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), S.Half)), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S.Half, S(3)
|
||
|
|
/2), ((1, 3, 2), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(-1, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(-3, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, S.Half)) )/2 + \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(3, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
2*sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S.Half, S(3)/
|
||
|
|
2), ((1, 3, 2), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), S.Half)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/6 + \
|
||
|
|
3*sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(-1, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, S.Half)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(-3, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S.Half, S(3)
|
||
|
|
/2), ((1, 3, 2), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(3, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S.Half, S(3)/
|
||
|
|
2), ((1, 3, 2), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), S.Half)), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, S.Half)) )/6 - \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(-1, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, S.Half)) )/6 - \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/6 - \
|
||
|
|
3*sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(Rational(3, 2), Rational(-3, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
-2*sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S.Half, S(3)
|
||
|
|
/2), ((1, 3, 2), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(3, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, S.Half)) )/2 - \
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), S.Half)), ((1, 3), (1, 2)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, S.Half)) )/6 - \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
1)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(-1, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
-JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 1), (1, 2, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S.Half, S(
|
||
|
|
3)/2), ((1, 3, 2), (1, 2, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(Rational(3, 2), Rational(-3, 2))), ((1, 3), (1, 2)) ) == \
|
||
|
|
JzKetCoupled(Rational(5, 2), -S(
|
||
|
|
5)/2, (S.Half, S.Half, Rational(3, 2)), ((1, 3, 2), (1, 2, Rational(5, 2))) )
|
||
|
|
|
||
|
|
|
||
|
|
def test_couple_4_states_numerical():
|
||
|
|
# Default coupling
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2, j4=1/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))) == \
|
||
|
|
JzKetCoupled(2, 2, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/3 - \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 0)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/3 + \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 1)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/6 - \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)),
|
||
|
|
JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half),
|
||
|
|
((1, 2, 0), (1, 3, S.Half), (1, 4, 0)))/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half),
|
||
|
|
((1, 2, 1), (1, 3, S.Half), (1, 4, 0)))/6 + \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half),
|
||
|
|
((1, 2, 0), (1, 3, S.Half), (1, 4, 1)))/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half),
|
||
|
|
((1, 2, 1), (1, 3, S.Half), (1, 4, 1)))/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half),
|
||
|
|
((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)))/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S.Half, S.Half, S.Half),
|
||
|
|
((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)))/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
-JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 0)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 0)) )/6 + \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 1)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/6 - \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 1)) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/6 - \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
-JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 0)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 0)) )/6 - \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 1)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 0)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 0)) )/6 - \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 1)) )/2 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/6 - \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (1, 3, S.Half), (1, 4, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/6 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 0)) )/3 - \
|
||
|
|
sqrt(3)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/3 - \
|
||
|
|
sqrt(6)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, S.Half), (1, 4, 1)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/6 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)))) == \
|
||
|
|
JzKetCoupled(2, -2, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, 2)) )
|
||
|
|
# j1=S.Half, S.Half, S.Half, 1
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1))) == \
|
||
|
|
JzKetCoupled(Rational(5, 2), Rational(5, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0))) == \
|
||
|
|
sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/3 + \
|
||
|
|
2*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))) == \
|
||
|
|
2*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 + \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/6 - \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 - \
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 + \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 - \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/6 - \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 + \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/6 - \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/3 - \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 - \
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1))) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/6 - \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 + \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))) == \
|
||
|
|
sqrt(3)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/6 - \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 - \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/6 - \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/3 - \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 + \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/6 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1))) == \
|
||
|
|
2*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 - \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/3 - \
|
||
|
|
2*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1))) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, S.Half), (1, 4, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1))) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, S.Half)) )/2 - \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0))) == \
|
||
|
|
-sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1))) == \
|
||
|
|
JzKetCoupled(Rational(5, 2), Rational(-5, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (1, 3, Rational(3, 2)), (1, 4, Rational(5, 2))) )
|
||
|
|
# Couple j1 to j2, j3 to j4
|
||
|
|
# j1=1/2, j2=1/2, j3=1/2, j4=1/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
JzKetCoupled(2, 2, (S(
|
||
|
|
1)/2, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 0), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 0), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 0)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 1), (1, 3, 1)) )/2 - \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 0), (1, 3, 0)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 0)) )/6 + \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 0), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 0), (1, 3, 0)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 0)) )/6 + \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 1), (1, 3, 1)) )/2 - \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 0), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 1), (1, 3, 1)) )/2 - \
|
||
|
|
JzKetCoupled(1, 1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, 1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 0), (1, 3, 0)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 0)) )/6 - \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 0), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 0), (1, 3, 0)) )/2 - \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 0)) )/6 - \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 1), (1, 3, 1)) )/2 - \
|
||
|
|
JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 0), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 0), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(0, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 0)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(1, 0, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
sqrt(6)*JzKetCoupled(2, 0, (S.Half, S.Half, S.Half, S.One/
|
||
|
|
2), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/6
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 0), (1, 3, 1)) )/2 - \
|
||
|
|
JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 0), (1, 3, 1)) )/2 - \
|
||
|
|
JzKetCoupled(1, -1, (S.Half, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 1)) )/2 + \
|
||
|
|
JzKetCoupled(2, -1, (S.Half, S(
|
||
|
|
1)/2, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )/2
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2))), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
JzKetCoupled(2, -2, (S(
|
||
|
|
1)/2, S.Half, S.Half, S.Half), ((1, 2, 1), (3, 4, 1), (1, 3, 2)) )
|
||
|
|
# j1=S.Half, S.Half, S.Half, 1
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
JzKetCoupled(Rational(5, 2), Rational(5, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
2*sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
2*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/3 - \
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
4*sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/2 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, S.Half), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/6 - \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/30 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/6 + \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/30 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, S.Half), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/6 - \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/3 + \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/2 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, 0)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(6)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, S.Half), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/6 - \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/3 - \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, S.Half), JzKet(1, -1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/6 + \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/30 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(3)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/3 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/30 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, S.Half), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/6 - \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/3 - \
|
||
|
|
sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 0), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/2 + \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/10 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/2 - \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(3, 2), S.Half, (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/5 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), S.Half, (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, 0)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/3 + \
|
||
|
|
JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
4*sqrt(5)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, S.Half), JzKet(1, -1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
sqrt(6)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
sqrt(30)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(5)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
2*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, S.Half)) )/3 + \
|
||
|
|
sqrt(2)*JzKetCoupled(S.Half, Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, S.Half)) )/6 - \
|
||
|
|
sqrt(2)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
2*sqrt(10)*JzKetCoupled(Rational(3, 2), Rational(-1, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-1, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/10
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, 0)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
-sqrt(3)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, S.Half), (1, 3, Rational(3, 2))) )/3 - \
|
||
|
|
2*sqrt(15)*JzKetCoupled(Rational(3, 2), Rational(-3, 2), (S.Half, S.Half, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(3, 2))) )/15 + \
|
||
|
|
sqrt(10)*JzKetCoupled(Rational(5, 2), Rational(-3, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )/5
|
||
|
|
assert couple(TensorProduct(JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(S.Half, Rational(-1, 2)), JzKet(1, -1)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
JzKetCoupled(Rational(5, 2), Rational(-5, 2), (S.Half, S(
|
||
|
|
1)/2, S.Half, 1), ((1, 2, 1), (3, 4, Rational(3, 2)), (1, 3, Rational(5, 2))) )
|
||
|
|
|
||
|
|
|
||
|
|
def test_couple_symbolic():
|
||
|
|
assert couple(TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
Sum(CG(j1, m1, j2, m2, j, m1 + m2) * JzKetCoupled(j, m1 + m2, (
|
||
|
|
j1, j2)), (j, m1 + m2, j1 + j2))
|
||
|
|
assert couple(TensorProduct(JzKet(j1, m1), JzKet(j2, m2), JzKet(j3, m3))) == \
|
||
|
|
Sum(CG(j1, m1, j2, m2, j12, m1 + m2) * CG(j12, m1 + m2, j3, m3, j, m1 + m2 + m3) *
|
||
|
|
JzKetCoupled(j, m1 + m2 + m3, (j1, j2, j3), ((1, 2, j12), (1, 3, j)) ),
|
||
|
|
(j12, m1 + m2, j1 + j2), (j, m1 + m2 + m3, j12 + j3))
|
||
|
|
assert couple(TensorProduct(JzKet(j1, m1), JzKet(j2, m2), JzKet(j3, m3)), ((1, 3), (1, 2)) ) == \
|
||
|
|
Sum(CG(j1, m1, j3, m3, j13, m1 + m3) * CG(j13, m1 + m3, j2, m2, j, m1 + m2 + m3) *
|
||
|
|
JzKetCoupled(j, m1 + m2 + m3, (j1, j2, j3), ((1, 3, j13), (1, 2, j)) ),
|
||
|
|
(j13, m1 + m3, j1 + j3), (j, m1 + m2 + m3, j13 + j2))
|
||
|
|
assert couple(TensorProduct(JzKet(j1, m1), JzKet(j2, m2), JzKet(j3, m3), JzKet(j4, m4))) == \
|
||
|
|
Sum(CG(j1, m1, j2, m2, j12, m1 + m2) * CG(j12, m1 + m2, j3, m3, j123, m1 + m2 + m3) * CG(j123, m1 + m2 + m3, j4, m4, j, m1 + m2 + m3 + m4) *
|
||
|
|
JzKetCoupled(j, m1 + m2 + m3 + m4, (
|
||
|
|
j1, j2, j3, j4), ((1, 2, j12), (1, 3, j123), (1, 4, j)) ),
|
||
|
|
(j12, m1 + m2, j1 + j2), (j123, m1 + m2 + m3, j12 + j3), (j, m1 + m2 + m3 + m4, j123 + j4))
|
||
|
|
assert couple(TensorProduct(JzKet(j1, m1), JzKet(j2, m2), JzKet(j3, m3), JzKet(j4, m4)), ((1, 2), (3, 4), (1, 3)) ) == \
|
||
|
|
Sum(CG(j1, m1, j2, m2, j12, m1 + m2) * CG(j3, m3, j4, m4, j34, m3 + m4) * CG(j12, m1 + m2, j34, m3 + m4, j, m1 + m2 + m3 + m4) *
|
||
|
|
JzKetCoupled(j, m1 + m2 + m3 + m4, (
|
||
|
|
j1, j2, j3, j4), ((1, 2, j12), (3, 4, j34), (1, 3, j)) ),
|
||
|
|
(j12, m1 + m2, j1 + j2), (j34, m3 + m4, j3 + j4), (j, m1 + m2 + m3 + m4, j12 + j34))
|
||
|
|
assert couple(TensorProduct(JzKet(j1, m1), JzKet(j2, m2), JzKet(j3, m3), JzKet(j4, m4)), ((1, 3), (1, 4), (1, 2)) ) == \
|
||
|
|
Sum(CG(j1, m1, j3, m3, j13, m1 + m3) * CG(j13, m1 + m3, j4, m4, j134, m1 + m3 + m4) * CG(j134, m1 + m3 + m4, j2, m2, j, m1 + m2 + m3 + m4) *
|
||
|
|
JzKetCoupled(j, m1 + m2 + m3 + m4, (
|
||
|
|
j1, j2, j3, j4), ((1, 3, j13), (1, 4, j134), (1, 2, j)) ),
|
||
|
|
(j13, m1 + m3, j1 + j3), (j134, m1 + m3 + m4, j13 + j4), (j, m1 + m2 + m3 + m4, j134 + j2))
|
||
|
|
|
||
|
|
|
||
|
|
def test_innerproduct():
|
||
|
|
assert InnerProduct(JzBra(1, 1), JzKet(1, 1)).doit() == 1
|
||
|
|
assert InnerProduct(
|
||
|
|
JzBra(S.Half, S.Half), JzKet(S.Half, Rational(-1, 2))).doit() == 0
|
||
|
|
assert InnerProduct(JzBra(j, m), JzKet(j, m)).doit() == 1
|
||
|
|
assert InnerProduct(JzBra(1, 0), JyKet(1, 1)).doit() == I/sqrt(2)
|
||
|
|
assert InnerProduct(
|
||
|
|
JxBra(S.Half, S.Half), JzKet(S.Half, S.Half)).doit() == -sqrt(2)/2
|
||
|
|
assert InnerProduct(JyBra(1, 1), JzKet(1, 1)).doit() == S.Half
|
||
|
|
assert InnerProduct(JxBra(1, -1), JyKet(1, 1)).doit() == 0
|
||
|
|
|
||
|
|
|
||
|
|
def test_rotation_small_d():
|
||
|
|
# Symbolic tests
|
||
|
|
# j = 1/2
|
||
|
|
assert Rotation.d(S.Half, S.Half, S.Half, beta).doit() == cos(beta/2)
|
||
|
|
assert Rotation.d(S.Half, S.Half, Rational(-1, 2), beta).doit() == -sin(beta/2)
|
||
|
|
assert Rotation.d(S.Half, Rational(-1, 2), S.Half, beta).doit() == sin(beta/2)
|
||
|
|
assert Rotation.d(S.Half, Rational(-1, 2), Rational(-1, 2), beta).doit() == cos(beta/2)
|
||
|
|
# j = 1
|
||
|
|
assert Rotation.d(1, 1, 1, beta).doit() == (1 + cos(beta))/2
|
||
|
|
assert Rotation.d(1, 1, 0, beta).doit() == -sin(beta)/sqrt(2)
|
||
|
|
assert Rotation.d(1, 1, -1, beta).doit() == (1 - cos(beta))/2
|
||
|
|
assert Rotation.d(1, 0, 1, beta).doit() == sin(beta)/sqrt(2)
|
||
|
|
assert Rotation.d(1, 0, 0, beta).doit() == cos(beta)
|
||
|
|
assert Rotation.d(1, 0, -1, beta).doit() == -sin(beta)/sqrt(2)
|
||
|
|
assert Rotation.d(1, -1, 1, beta).doit() == (1 - cos(beta))/2
|
||
|
|
assert Rotation.d(1, -1, 0, beta).doit() == sin(beta)/sqrt(2)
|
||
|
|
assert Rotation.d(1, -1, -1, beta).doit() == (1 + cos(beta))/2
|
||
|
|
# j = 3/2
|
||
|
|
assert Rotation.d(S(
|
||
|
|
3)/2, Rational(3, 2), Rational(3, 2), beta).doit() == (3*cos(beta/2) + cos(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), S(
|
||
|
|
3)/2, S.Half, beta).doit() == -sqrt(3)*(sin(beta/2) + sin(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), S(
|
||
|
|
3)/2, Rational(-1, 2), beta).doit() == sqrt(3)*(cos(beta/2) - cos(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), S(
|
||
|
|
3)/2, Rational(-3, 2), beta).doit() == (-3*sin(beta/2) + sin(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), S(
|
||
|
|
1)/2, Rational(3, 2), beta).doit() == sqrt(3)*(sin(beta/2) + sin(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(S(
|
||
|
|
3)/2, S.Half, S.Half, beta).doit() == (cos(beta/2) + 3*cos(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(S(
|
||
|
|
3)/2, S.Half, Rational(-1, 2), beta).doit() == (sin(beta/2) - 3*sin(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), S(
|
||
|
|
1)/2, Rational(-3, 2), beta).doit() == sqrt(3)*(cos(beta/2) - cos(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), -S(
|
||
|
|
1)/2, Rational(3, 2), beta).doit() == sqrt(3)*(cos(beta/2) - cos(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), -S(
|
||
|
|
1)/2, S.Half, beta).doit() == (-sin(beta/2) + 3*sin(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), -S(
|
||
|
|
1)/2, Rational(-1, 2), beta).doit() == (cos(beta/2) + 3*cos(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), -S(
|
||
|
|
1)/2, Rational(-3, 2), beta).doit() == -sqrt(3)*(sin(beta/2) + sin(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(S(
|
||
|
|
3)/2, Rational(-3, 2), Rational(3, 2), beta).doit() == (3*sin(beta/2) - sin(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), -S(
|
||
|
|
3)/2, S.Half, beta).doit() == sqrt(3)*(cos(beta/2) - cos(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), -S(
|
||
|
|
3)/2, Rational(-1, 2), beta).doit() == sqrt(3)*(sin(beta/2) + sin(beta*Rational(3, 2)))/4
|
||
|
|
assert Rotation.d(Rational(3, 2), -S(
|
||
|
|
3)/2, Rational(-3, 2), beta).doit() == (3*cos(beta/2) + cos(beta*Rational(3, 2)))/4
|
||
|
|
# j = 2
|
||
|
|
assert Rotation.d(2, 2, 2, beta).doit() == (3 + 4*cos(beta) + cos(2*beta))/8
|
||
|
|
assert Rotation.d(2, 2, 1, beta).doit() == -((cos(beta) + 1)*sin(beta))/2
|
||
|
|
assert Rotation.d(2, 2, 0, beta).doit() == sqrt(6)*sin(beta)**2/4
|
||
|
|
assert Rotation.d(2, 2, -1, beta).doit() == (cos(beta) - 1)*sin(beta)/2
|
||
|
|
assert Rotation.d(2, 2, -2, beta).doit() == (3 - 4*cos(beta) + cos(2*beta))/8
|
||
|
|
assert Rotation.d(2, 1, 2, beta).doit() == (cos(beta) + 1)*sin(beta)/2
|
||
|
|
assert Rotation.d(2, 1, 1, beta).doit() == (cos(beta) + cos(2*beta))/2
|
||
|
|
assert Rotation.d(2, 1, 0, beta).doit() == -sqrt(6)*sin(2*beta)/4
|
||
|
|
assert Rotation.d(2, 1, -1, beta).doit() == (cos(beta) - cos(2*beta))/2
|
||
|
|
assert Rotation.d(2, 1, -2, beta).doit() == (cos(beta) - 1)*sin(beta)/2
|
||
|
|
assert Rotation.d(2, 0, 2, beta).doit() == sqrt(6)*sin(beta)**2/4
|
||
|
|
assert Rotation.d(2, 0, 1, beta).doit() == sqrt(6)*sin(2*beta)/4
|
||
|
|
assert Rotation.d(2, 0, 0, beta).doit() == (1 + 3*cos(2*beta))/4
|
||
|
|
assert Rotation.d(2, 0, -1, beta).doit() == -sqrt(6)*sin(2*beta)/4
|
||
|
|
assert Rotation.d(2, 0, -2, beta).doit() == sqrt(6)*sin(beta)**2/4
|
||
|
|
assert Rotation.d(2, -1, 2, beta).doit() == (2*sin(beta) - sin(2*beta))/4
|
||
|
|
assert Rotation.d(2, -1, 1, beta).doit() == (cos(beta) - cos(2*beta))/2
|
||
|
|
assert Rotation.d(2, -1, 0, beta).doit() == sqrt(6)*sin(2*beta)/4
|
||
|
|
assert Rotation.d(2, -1, -1, beta).doit() == (cos(beta) + cos(2*beta))/2
|
||
|
|
assert Rotation.d(2, -1, -2, beta).doit() == -((cos(beta) + 1)*sin(beta))/2
|
||
|
|
assert Rotation.d(2, -2, 2, beta).doit() == (3 - 4*cos(beta) + cos(2*beta))/8
|
||
|
|
assert Rotation.d(2, -2, 1, beta).doit() == (2*sin(beta) - sin(2*beta))/4
|
||
|
|
assert Rotation.d(2, -2, 0, beta).doit() == sqrt(6)*sin(beta)**2/4
|
||
|
|
assert Rotation.d(2, -2, -1, beta).doit() == (cos(beta) + 1)*sin(beta)/2
|
||
|
|
assert Rotation.d(2, -2, -2, beta).doit() == (3 + 4*cos(beta) + cos(2*beta))/8
|
||
|
|
# Numerical tests
|
||
|
|
# j = 1/2
|
||
|
|
assert Rotation.d(S.Half, S.Half, S.Half, pi/2).doit() == sqrt(2)/2
|
||
|
|
assert Rotation.d(S.Half, S.Half, Rational(-1, 2), pi/2).doit() == -sqrt(2)/2
|
||
|
|
assert Rotation.d(S.Half, Rational(-1, 2), S.Half, pi/2).doit() == sqrt(2)/2
|
||
|
|
assert Rotation.d(S.Half, Rational(-1, 2), Rational(-1, 2), pi/2).doit() == sqrt(2)/2
|
||
|
|
# j = 1
|
||
|
|
assert Rotation.d(1, 1, 1, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.d(1, 1, 0, pi/2).doit() == -sqrt(2)/2
|
||
|
|
assert Rotation.d(1, 1, -1, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.d(1, 0, 1, pi/2).doit() == sqrt(2)/2
|
||
|
|
assert Rotation.d(1, 0, 0, pi/2).doit() == 0
|
||
|
|
assert Rotation.d(1, 0, -1, pi/2).doit() == -sqrt(2)/2
|
||
|
|
assert Rotation.d(1, -1, 1, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.d(1, -1, 0, pi/2).doit() == sqrt(2)/2
|
||
|
|
assert Rotation.d(1, -1, -1, pi/2).doit() == S.Half
|
||
|
|
# j = 3/2
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(3, 2), Rational(3, 2), pi/2).doit() == sqrt(2)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(3, 2), S.Half, pi/2).doit() == -sqrt(6)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(3, 2), Rational(-1, 2), pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(3, 2), Rational(-3, 2), pi/2).doit() == -sqrt(2)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), S.Half, Rational(3, 2), pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), S.Half, S.Half, pi/2).doit() == -sqrt(2)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), S.Half, Rational(-1, 2), pi/2).doit() == -sqrt(2)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), S.Half, Rational(-3, 2), pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(-1, 2), Rational(3, 2), pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(-1, 2), S.Half, pi/2).doit() == sqrt(2)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(-1, 2), Rational(-1, 2), pi/2).doit() == -sqrt(2)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(-1, 2), Rational(-3, 2), pi/2).doit() == -sqrt(6)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(-3, 2), Rational(3, 2), pi/2).doit() == sqrt(2)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(-3, 2), S.Half, pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(-3, 2), Rational(-1, 2), pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(Rational(3, 2), Rational(-3, 2), Rational(-3, 2), pi/2).doit() == sqrt(2)/4
|
||
|
|
# j = 2
|
||
|
|
assert Rotation.d(2, 2, 2, pi/2).doit() == Rational(1, 4)
|
||
|
|
assert Rotation.d(2, 2, 1, pi/2).doit() == Rational(-1, 2)
|
||
|
|
assert Rotation.d(2, 2, 0, pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(2, 2, -1, pi/2).doit() == Rational(-1, 2)
|
||
|
|
assert Rotation.d(2, 2, -2, pi/2).doit() == Rational(1, 4)
|
||
|
|
assert Rotation.d(2, 1, 2, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.d(2, 1, 1, pi/2).doit() == Rational(-1, 2)
|
||
|
|
assert Rotation.d(2, 1, 0, pi/2).doit() == 0
|
||
|
|
assert Rotation.d(2, 1, -1, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.d(2, 1, -2, pi/2).doit() == Rational(-1, 2)
|
||
|
|
assert Rotation.d(2, 0, 2, pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(2, 0, 1, pi/2).doit() == 0
|
||
|
|
assert Rotation.d(2, 0, 0, pi/2).doit() == Rational(-1, 2)
|
||
|
|
assert Rotation.d(2, 0, -1, pi/2).doit() == 0
|
||
|
|
assert Rotation.d(2, 0, -2, pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(2, -1, 2, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.d(2, -1, 1, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.d(2, -1, 0, pi/2).doit() == 0
|
||
|
|
assert Rotation.d(2, -1, -1, pi/2).doit() == Rational(-1, 2)
|
||
|
|
assert Rotation.d(2, -1, -2, pi/2).doit() == Rational(-1, 2)
|
||
|
|
assert Rotation.d(2, -2, 2, pi/2).doit() == Rational(1, 4)
|
||
|
|
assert Rotation.d(2, -2, 1, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.d(2, -2, 0, pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.d(2, -2, -1, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.d(2, -2, -2, pi/2).doit() == Rational(1, 4)
|
||
|
|
|
||
|
|
|
||
|
|
def test_rotation_d():
|
||
|
|
# Symbolic tests
|
||
|
|
# j = 1/2
|
||
|
|
assert Rotation.D(S.Half, S.Half, S.Half, alpha, beta, gamma).doit() == \
|
||
|
|
cos(beta/2)*exp(-I*alpha/2)*exp(-I*gamma/2)
|
||
|
|
assert Rotation.D(S.Half, S.Half, Rational(-1, 2), alpha, beta, gamma).doit() == \
|
||
|
|
-sin(beta/2)*exp(-I*alpha/2)*exp(I*gamma/2)
|
||
|
|
assert Rotation.D(S.Half, Rational(-1, 2), S.Half, alpha, beta, gamma).doit() == \
|
||
|
|
sin(beta/2)*exp(I*alpha/2)*exp(-I*gamma/2)
|
||
|
|
assert Rotation.D(S.Half, Rational(-1, 2), Rational(-1, 2), alpha, beta, gamma).doit() == \
|
||
|
|
cos(beta/2)*exp(I*alpha/2)*exp(I*gamma/2)
|
||
|
|
# j = 1
|
||
|
|
assert Rotation.D(1, 1, 1, alpha, beta, gamma).doit() == \
|
||
|
|
(1 + cos(beta))/2*exp(-I*alpha)*exp(-I*gamma)
|
||
|
|
assert Rotation.D(1, 1, 0, alpha, beta, gamma).doit() == -sin(
|
||
|
|
beta)/sqrt(2)*exp(-I*alpha)
|
||
|
|
assert Rotation.D(1, 1, -1, alpha, beta, gamma).doit() == \
|
||
|
|
(1 - cos(beta))/2*exp(-I*alpha)*exp(I*gamma)
|
||
|
|
assert Rotation.D(1, 0, 1, alpha, beta, gamma).doit() == \
|
||
|
|
sin(beta)/sqrt(2)*exp(-I*gamma)
|
||
|
|
assert Rotation.D(1, 0, 0, alpha, beta, gamma).doit() == cos(beta)
|
||
|
|
assert Rotation.D(1, 0, -1, alpha, beta, gamma).doit() == \
|
||
|
|
-sin(beta)/sqrt(2)*exp(I*gamma)
|
||
|
|
assert Rotation.D(1, -1, 1, alpha, beta, gamma).doit() == \
|
||
|
|
(1 - cos(beta))/2*exp(I*alpha)*exp(-I*gamma)
|
||
|
|
assert Rotation.D(1, -1, 0, alpha, beta, gamma).doit() == \
|
||
|
|
sin(beta)/sqrt(2)*exp(I*alpha)
|
||
|
|
assert Rotation.D(1, -1, -1, alpha, beta, gamma).doit() == \
|
||
|
|
(1 + cos(beta))/2*exp(I*alpha)*exp(I*gamma)
|
||
|
|
# j = 3/2
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(3, 2), Rational(3, 2), alpha, beta, gamma).doit() == \
|
||
|
|
(3*cos(beta/2) + cos(beta*Rational(3, 2)))/4*exp(I*alpha*Rational(-3, 2))*exp(I*gamma*Rational(-3, 2))
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(3, 2), S.Half, alpha, beta, gamma).doit() == \
|
||
|
|
-sqrt(3)*(sin(beta/2) + sin(beta*Rational(3, 2)))/4*exp(I*alpha*Rational(-3, 2))*exp(-I*gamma/2)
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(3, 2), Rational(-1, 2), alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(3)*(cos(beta/2) - cos(beta*Rational(3, 2)))/4*exp(I*alpha*Rational(-3, 2))*exp(I*gamma/2)
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(3, 2), Rational(-3, 2), alpha, beta, gamma).doit() == \
|
||
|
|
(-3*sin(beta/2) + sin(beta*Rational(3, 2)))/4*exp(I*alpha*Rational(-3, 2))*exp(I*gamma*Rational(3, 2))
|
||
|
|
assert Rotation.D(Rational(3, 2), S.Half, Rational(3, 2), alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(3)*(sin(beta/2) + sin(beta*Rational(3, 2)))/4*exp(-I*alpha/2)*exp(I*gamma*Rational(-3, 2))
|
||
|
|
assert Rotation.D(Rational(3, 2), S.Half, S.Half, alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta/2) + 3*cos(beta*Rational(3, 2)))/4*exp(-I*alpha/2)*exp(-I*gamma/2)
|
||
|
|
assert Rotation.D(Rational(3, 2), S.Half, Rational(-1, 2), alpha, beta, gamma).doit() == \
|
||
|
|
(sin(beta/2) - 3*sin(beta*Rational(3, 2)))/4*exp(-I*alpha/2)*exp(I*gamma/2)
|
||
|
|
assert Rotation.D(Rational(3, 2), S.Half, Rational(-3, 2), alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(3)*(cos(beta/2) - cos(beta*Rational(3, 2)))/4*exp(-I*alpha/2)*exp(I*gamma*Rational(3, 2))
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(-1, 2), Rational(3, 2), alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(3)*(cos(beta/2) - cos(beta*Rational(3, 2)))/4*exp(I*alpha/2)*exp(I*gamma*Rational(-3, 2))
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(-1, 2), S.Half, alpha, beta, gamma).doit() == \
|
||
|
|
(-sin(beta/2) + 3*sin(beta*Rational(3, 2)))/4*exp(I*alpha/2)*exp(-I*gamma/2)
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(-1, 2), Rational(-1, 2), alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta/2) + 3*cos(beta*Rational(3, 2)))/4*exp(I*alpha/2)*exp(I*gamma/2)
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(-1, 2), Rational(-3, 2), alpha, beta, gamma).doit() == \
|
||
|
|
-sqrt(3)*(sin(beta/2) + sin(beta*Rational(3, 2)))/4*exp(I*alpha/2)*exp(I*gamma*Rational(3, 2))
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(-3, 2), Rational(3, 2), alpha, beta, gamma).doit() == \
|
||
|
|
(3*sin(beta/2) - sin(beta*Rational(3, 2)))/4*exp(I*alpha*Rational(3, 2))*exp(I*gamma*Rational(-3, 2))
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(-3, 2), S.Half, alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(3)*(cos(beta/2) - cos(beta*Rational(3, 2)))/4*exp(I*alpha*Rational(3, 2))*exp(-I*gamma/2)
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(-3, 2), Rational(-1, 2), alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(3)*(sin(beta/2) + sin(beta*Rational(3, 2)))/4*exp(I*alpha*Rational(3, 2))*exp(I*gamma/2)
|
||
|
|
assert Rotation.D(Rational(3, 2), Rational(-3, 2), Rational(-3, 2), alpha, beta, gamma).doit() == \
|
||
|
|
(3*cos(beta/2) + cos(beta*Rational(3, 2)))/4*exp(I*alpha*Rational(3, 2))*exp(I*gamma*Rational(3, 2))
|
||
|
|
# j = 2
|
||
|
|
assert Rotation.D(2, 2, 2, alpha, beta, gamma).doit() == \
|
||
|
|
(3 + 4*cos(beta) + cos(2*beta))/8*exp(-2*I*alpha)*exp(-2*I*gamma)
|
||
|
|
assert Rotation.D(2, 2, 1, alpha, beta, gamma).doit() == \
|
||
|
|
-((cos(beta) + 1)*exp(-2*I*alpha)*exp(-I*gamma)*sin(beta))/2
|
||
|
|
assert Rotation.D(2, 2, 0, alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(6)*sin(beta)**2/4*exp(-2*I*alpha)
|
||
|
|
assert Rotation.D(2, 2, -1, alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta) - 1)*sin(beta)/2*exp(-2*I*alpha)*exp(I*gamma)
|
||
|
|
assert Rotation.D(2, 2, -2, alpha, beta, gamma).doit() == \
|
||
|
|
(3 - 4*cos(beta) + cos(2*beta))/8*exp(-2*I*alpha)*exp(2*I*gamma)
|
||
|
|
assert Rotation.D(2, 1, 2, alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta) + 1)*sin(beta)/2*exp(-I*alpha)*exp(-2*I*gamma)
|
||
|
|
assert Rotation.D(2, 1, 1, alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta) + cos(2*beta))/2*exp(-I*alpha)*exp(-I*gamma)
|
||
|
|
assert Rotation.D(2, 1, 0, alpha, beta, gamma).doit() == -sqrt(6)* \
|
||
|
|
sin(2*beta)/4*exp(-I*alpha)
|
||
|
|
assert Rotation.D(2, 1, -1, alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta) - cos(2*beta))/2*exp(-I*alpha)*exp(I*gamma)
|
||
|
|
assert Rotation.D(2, 1, -2, alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta) - 1)*sin(beta)/2*exp(-I*alpha)*exp(2*I*gamma)
|
||
|
|
assert Rotation.D(2, 0, 2, alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(6)*sin(beta)**2/4*exp(-2*I*gamma)
|
||
|
|
assert Rotation.D(2, 0, 1, alpha, beta, gamma).doit() == sqrt(6)* \
|
||
|
|
sin(2*beta)/4*exp(-I*gamma)
|
||
|
|
assert Rotation.D(
|
||
|
|
2, 0, 0, alpha, beta, gamma).doit() == (1 + 3*cos(2*beta))/4
|
||
|
|
assert Rotation.D(2, 0, -1, alpha, beta, gamma).doit() == -sqrt(6)* \
|
||
|
|
sin(2*beta)/4*exp(I*gamma)
|
||
|
|
assert Rotation.D(2, 0, -2, alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(6)*sin(beta)**2/4*exp(2*I*gamma)
|
||
|
|
assert Rotation.D(2, -1, 2, alpha, beta, gamma).doit() == \
|
||
|
|
(2*sin(beta) - sin(2*beta))/4*exp(I*alpha)*exp(-2*I*gamma)
|
||
|
|
assert Rotation.D(2, -1, 1, alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta) - cos(2*beta))/2*exp(I*alpha)*exp(-I*gamma)
|
||
|
|
assert Rotation.D(2, -1, 0, alpha, beta, gamma).doit() == sqrt(6)* \
|
||
|
|
sin(2*beta)/4*exp(I*alpha)
|
||
|
|
assert Rotation.D(2, -1, -1, alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta) + cos(2*beta))/2*exp(I*alpha)*exp(I*gamma)
|
||
|
|
assert Rotation.D(2, -1, -2, alpha, beta, gamma).doit() == \
|
||
|
|
-((cos(beta) + 1)*sin(beta))/2*exp(I*alpha)*exp(2*I*gamma)
|
||
|
|
assert Rotation.D(2, -2, 2, alpha, beta, gamma).doit() == \
|
||
|
|
(3 - 4*cos(beta) + cos(2*beta))/8*exp(2*I*alpha)*exp(-2*I*gamma)
|
||
|
|
assert Rotation.D(2, -2, 1, alpha, beta, gamma).doit() == \
|
||
|
|
(2*sin(beta) - sin(2*beta))/4*exp(2*I*alpha)*exp(-I*gamma)
|
||
|
|
assert Rotation.D(2, -2, 0, alpha, beta, gamma).doit() == \
|
||
|
|
sqrt(6)*sin(beta)**2/4*exp(2*I*alpha)
|
||
|
|
assert Rotation.D(2, -2, -1, alpha, beta, gamma).doit() == \
|
||
|
|
(cos(beta) + 1)*sin(beta)/2*exp(2*I*alpha)*exp(I*gamma)
|
||
|
|
assert Rotation.D(2, -2, -2, alpha, beta, gamma).doit() == \
|
||
|
|
(3 + 4*cos(beta) + cos(2*beta))/8*exp(2*I*alpha)*exp(2*I*gamma)
|
||
|
|
# Numerical tests
|
||
|
|
# j = 1/2
|
||
|
|
assert Rotation.D(
|
||
|
|
S.Half, S.Half, S.Half, pi/2, pi/2, pi/2).doit() == -I*sqrt(2)/2
|
||
|
|
assert Rotation.D(
|
||
|
|
S.Half, S.Half, Rational(-1, 2), pi/2, pi/2, pi/2).doit() == -sqrt(2)/2
|
||
|
|
assert Rotation.D(
|
||
|
|
S.Half, Rational(-1, 2), S.Half, pi/2, pi/2, pi/2).doit() == sqrt(2)/2
|
||
|
|
assert Rotation.D(
|
||
|
|
S.Half, Rational(-1, 2), Rational(-1, 2), pi/2, pi/2, pi/2).doit() == I*sqrt(2)/2
|
||
|
|
# j = 1
|
||
|
|
assert Rotation.D(1, 1, 1, pi/2, pi/2, pi/2).doit() == Rational(-1, 2)
|
||
|
|
assert Rotation.D(1, 1, 0, pi/2, pi/2, pi/2).doit() == I*sqrt(2)/2
|
||
|
|
assert Rotation.D(1, 1, -1, pi/2, pi/2, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.D(1, 0, 1, pi/2, pi/2, pi/2).doit() == -I*sqrt(2)/2
|
||
|
|
assert Rotation.D(1, 0, 0, pi/2, pi/2, pi/2).doit() == 0
|
||
|
|
assert Rotation.D(1, 0, -1, pi/2, pi/2, pi/2).doit() == -I*sqrt(2)/2
|
||
|
|
assert Rotation.D(1, -1, 1, pi/2, pi/2, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.D(1, -1, 0, pi/2, pi/2, pi/2).doit() == I*sqrt(2)/2
|
||
|
|
assert Rotation.D(1, -1, -1, pi/2, pi/2, pi/2).doit() == Rational(-1, 2)
|
||
|
|
# j = 3/2
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(3, 2), Rational(3, 2), pi/2, pi/2, pi/2).doit() == I*sqrt(2)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(3, 2), S.Half, pi/2, pi/2, pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(3, 2), Rational(-1, 2), pi/2, pi/2, pi/2).doit() == -I*sqrt(6)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(3, 2), Rational(-3, 2), pi/2, pi/2, pi/2).doit() == -sqrt(2)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), S.Half, Rational(3, 2), pi/2, pi/2, pi/2).doit() == -sqrt(6)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), S.Half, S.Half, pi/2, pi/2, pi/2).doit() == I*sqrt(2)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), S.Half, Rational(-1, 2), pi/2, pi/2, pi/2).doit() == -sqrt(2)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), S.Half, Rational(-3, 2), pi/2, pi/2, pi/2).doit() == I*sqrt(6)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(-1, 2), Rational(3, 2), pi/2, pi/2, pi/2).doit() == -I*sqrt(6)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(-1, 2), S.Half, pi/2, pi/2, pi/2).doit() == sqrt(2)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(-1, 2), Rational(-1, 2), pi/2, pi/2, pi/2).doit() == -I*sqrt(2)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(-1, 2), Rational(-3, 2), pi/2, pi/2, pi/2).doit() == sqrt(6)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(-3, 2), Rational(3, 2), pi/2, pi/2, pi/2).doit() == sqrt(2)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(-3, 2), S.Half, pi/2, pi/2, pi/2).doit() == I*sqrt(6)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(-3, 2), Rational(-1, 2), pi/2, pi/2, pi/2).doit() == -sqrt(6)/4
|
||
|
|
assert Rotation.D(
|
||
|
|
Rational(3, 2), Rational(-3, 2), Rational(-3, 2), pi/2, pi/2, pi/2).doit() == -I*sqrt(2)/4
|
||
|
|
# j = 2
|
||
|
|
assert Rotation.D(2, 2, 2, pi/2, pi/2, pi/2).doit() == Rational(1, 4)
|
||
|
|
assert Rotation.D(2, 2, 1, pi/2, pi/2, pi/2).doit() == -I/2
|
||
|
|
assert Rotation.D(2, 2, 0, pi/2, pi/2, pi/2).doit() == -sqrt(6)/4
|
||
|
|
assert Rotation.D(2, 2, -1, pi/2, pi/2, pi/2).doit() == I/2
|
||
|
|
assert Rotation.D(2, 2, -2, pi/2, pi/2, pi/2).doit() == Rational(1, 4)
|
||
|
|
assert Rotation.D(2, 1, 2, pi/2, pi/2, pi/2).doit() == I/2
|
||
|
|
assert Rotation.D(2, 1, 1, pi/2, pi/2, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.D(2, 1, 0, pi/2, pi/2, pi/2).doit() == 0
|
||
|
|
assert Rotation.D(2, 1, -1, pi/2, pi/2, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.D(2, 1, -2, pi/2, pi/2, pi/2).doit() == -I/2
|
||
|
|
assert Rotation.D(2, 0, 2, pi/2, pi/2, pi/2).doit() == -sqrt(6)/4
|
||
|
|
assert Rotation.D(2, 0, 1, pi/2, pi/2, pi/2).doit() == 0
|
||
|
|
assert Rotation.D(2, 0, 0, pi/2, pi/2, pi/2).doit() == Rational(-1, 2)
|
||
|
|
assert Rotation.D(2, 0, -1, pi/2, pi/2, pi/2).doit() == 0
|
||
|
|
assert Rotation.D(2, 0, -2, pi/2, pi/2, pi/2).doit() == -sqrt(6)/4
|
||
|
|
assert Rotation.D(2, -1, 2, pi/2, pi/2, pi/2).doit() == -I/2
|
||
|
|
assert Rotation.D(2, -1, 1, pi/2, pi/2, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.D(2, -1, 0, pi/2, pi/2, pi/2).doit() == 0
|
||
|
|
assert Rotation.D(2, -1, -1, pi/2, pi/2, pi/2).doit() == S.Half
|
||
|
|
assert Rotation.D(2, -1, -2, pi/2, pi/2, pi/2).doit() == I/2
|
||
|
|
assert Rotation.D(2, -2, 2, pi/2, pi/2, pi/2).doit() == Rational(1, 4)
|
||
|
|
assert Rotation.D(2, -2, 1, pi/2, pi/2, pi/2).doit() == I/2
|
||
|
|
assert Rotation.D(2, -2, 0, pi/2, pi/2, pi/2).doit() == -sqrt(6)/4
|
||
|
|
assert Rotation.D(2, -2, -1, pi/2, pi/2, pi/2).doit() == -I/2
|
||
|
|
assert Rotation.D(2, -2, -2, pi/2, pi/2, pi/2).doit() == Rational(1, 4)
|
||
|
|
|
||
|
|
|
||
|
|
def test_wignerd():
|
||
|
|
assert Rotation.D(
|
||
|
|
j, m, mp, alpha, beta, gamma) == WignerD(j, m, mp, alpha, beta, gamma)
|
||
|
|
assert Rotation.d(j, m, mp, beta) == WignerD(j, m, mp, 0, beta, 0)
|
||
|
|
|
||
|
|
def test_wignerD():
|
||
|
|
i,j=symbols('i j')
|
||
|
|
assert Rotation.D(1, 1, 1, 0, 0, 0) == WignerD(1, 1, 1, 0, 0, 0)
|
||
|
|
assert Rotation.D(1, 1, 2, 0, 0, 0) == WignerD(1, 1, 2, 0, 0, 0)
|
||
|
|
assert Rotation.D(1, i**2 - j**2, i**2 - j**2, 0, 0, 0) == WignerD(1, i**2 - j**2, i**2 - j**2, 0, 0, 0)
|
||
|
|
assert Rotation.D(1, i, i, 0, 0, 0) == WignerD(1, i, i, 0, 0, 0)
|
||
|
|
assert Rotation.D(1, i, i+1, 0, 0, 0) == WignerD(1, i, i+1, 0, 0, 0)
|
||
|
|
assert Rotation.D(1, 0, 0, 0, 0, 0) == WignerD(1, 0, 0, 0, 0, 0)
|
||
|
|
|
||
|
|
def test_jplus():
|
||
|
|
assert Commutator(Jplus, Jminus).doit() == 2*hbar*Jz
|
||
|
|
assert Jplus.matrix_element(1, 1, 1, 1) == 0
|
||
|
|
assert Jplus.rewrite('xyz') == Jx + I*Jy
|
||
|
|
# Normal operators, normal states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jplus*JxKet(1, 1)) == \
|
||
|
|
-hbar*sqrt(2)*JxKet(1, 0)/2 + hbar*JxKet(1, 1)
|
||
|
|
assert qapply(Jplus*JyKet(1, 1)) == \
|
||
|
|
hbar*sqrt(2)*JyKet(1, 0)/2 + I*hbar*JyKet(1, 1)
|
||
|
|
assert qapply(Jplus*JzKet(1, 1)) == 0
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jplus*JxKet(j, m)) == \
|
||
|
|
Sum(hbar * sqrt(-mi**2 - mi + j**2 + j) * WignerD(j, mi, m, 0, pi/2, 0) *
|
||
|
|
Sum(WignerD(j, mi1, mi + 1, 0, pi*Rational(3, 2), 0) * JxKet(j, mi1),
|
||
|
|
(mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jplus*JyKet(j, m)) == \
|
||
|
|
Sum(hbar * sqrt(j**2 + j - mi**2 - mi) * WignerD(j, mi, m, pi*Rational(3, 2), -pi/2, pi/2) *
|
||
|
|
Sum(WignerD(j, mi1, mi + 1, pi*Rational(3, 2), pi/2, pi/2) * JyKet(j, mi1),
|
||
|
|
(mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jplus*JzKet(j, m)) == \
|
||
|
|
hbar*sqrt(j**2 + j - m**2 - m)*JzKet(j, m + 1)
|
||
|
|
# Normal operators, coupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jplus*JxKetCoupled(1, 1, (1, 1))) == -hbar*sqrt(2) * \
|
||
|
|
JxKetCoupled(1, 0, (1, 1))/2 + hbar*JxKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(Jplus*JyKetCoupled(1, 1, (1, 1))) == hbar*sqrt(2) * \
|
||
|
|
JyKetCoupled(1, 0, (1, 1))/2 + I*hbar*JyKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(Jplus*JzKet(1, 1)) == 0
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jplus*JxKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
Sum(hbar * sqrt(-mi**2 - mi + j**2 + j) * WignerD(j, mi, m, 0, pi/2, 0) *
|
||
|
|
Sum(
|
||
|
|
WignerD(
|
||
|
|
j, mi1, mi + 1, 0, pi*Rational(3, 2), 0) * JxKetCoupled(j, mi1, (j1, j2)),
|
||
|
|
(mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jplus*JyKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
Sum(hbar * sqrt(j**2 + j - mi**2 - mi) * WignerD(j, mi, m, pi*Rational(3, 2), -pi/2, pi/2) *
|
||
|
|
Sum(
|
||
|
|
WignerD(j, mi1, mi + 1, pi*Rational(3, 2), pi/2, pi/2) *
|
||
|
|
JyKetCoupled(j, mi1, (j1, j2)),
|
||
|
|
(mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jplus*JzKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
hbar*sqrt(j**2 + j - m**2 - m)*JzKetCoupled(j, m + 1, (j1, j2))
|
||
|
|
# Uncoupled operators, uncoupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(TensorProduct(Jplus, 1)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
-hbar*sqrt(2)*TensorProduct(JxKet(1, 0), JxKet(1, -1))/2 + \
|
||
|
|
hbar*TensorProduct(JxKet(1, 1), JxKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, Jplus)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
-hbar*TensorProduct(JxKet(1, 1), JxKet(1, -1)) + \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JxKet(1, 1), JxKet(1, 0))/2
|
||
|
|
assert qapply(TensorProduct(Jplus, 1)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JyKet(1, 0), JyKet(1, -1))/2 + \
|
||
|
|
hbar*I*TensorProduct(JyKet(1, 1), JyKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, Jplus)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
-hbar*I*TensorProduct(JyKet(1, 1), JyKet(1, -1)) + \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JyKet(1, 1), JyKet(1, 0))/2
|
||
|
|
assert qapply(
|
||
|
|
TensorProduct(Jplus, 1)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == 0
|
||
|
|
assert qapply(TensorProduct(1, Jplus)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JzKet(1, 1), JzKet(1, 0))
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(TensorProduct(Jplus, 1)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(Sum(hbar * sqrt(-mi**2 - mi + j1**2 + j1) * WignerD(j1, mi, m1, 0, pi/2, 0) *
|
||
|
|
Sum(WignerD(j1, mi1, mi + 1, 0, pi*Rational(3, 2), 0) * JxKet(j1, mi1),
|
||
|
|
(mi1, -j1, j1)), (mi, -j1, j1)), JxKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jplus)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(JxKet(j1, m1), Sum(hbar * sqrt(-mi**2 - mi + j2**2 + j2) * WignerD(j2, mi, m2, 0, pi/2, 0) *
|
||
|
|
Sum(WignerD(j2, mi1, mi + 1, 0, pi*Rational(3, 2), 0) * JxKet(j2, mi1),
|
||
|
|
(mi1, -j2, j2)), (mi, -j2, j2)))
|
||
|
|
assert qapply(TensorProduct(Jplus, 1)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(Sum(hbar * sqrt(j1**2 + j1 - mi**2 - mi) * WignerD(j1, mi, m1, pi*Rational(3, 2), -pi/2, pi/2) *
|
||
|
|
Sum(WignerD(j1, mi1, mi + 1, pi*Rational(3, 2), pi/2, pi/2) * JyKet(j1, mi1),
|
||
|
|
(mi1, -j1, j1)), (mi, -j1, j1)), JyKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jplus)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(JyKet(j1, m1), Sum(hbar * sqrt(j2**2 + j2 - mi**2 - mi) * WignerD(j2, mi, m2, pi*Rational(3, 2), -pi/2, pi/2) *
|
||
|
|
Sum(WignerD(j2, mi1, mi + 1, pi*Rational(3, 2), pi/2, pi/2) * JyKet(j2, mi1),
|
||
|
|
(mi1, -j2, j2)), (mi, -j2, j2)))
|
||
|
|
assert qapply(TensorProduct(Jplus, 1)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*sqrt(
|
||
|
|
j1**2 + j1 - m1**2 - m1)*TensorProduct(JzKet(j1, m1 + 1), JzKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jplus)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*sqrt(
|
||
|
|
j2**2 + j2 - m2**2 - m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 + 1))
|
||
|
|
|
||
|
|
|
||
|
|
def test_jminus():
|
||
|
|
assert qapply(Jminus*JzKet(1, -1)) == 0
|
||
|
|
assert Jminus.matrix_element(1, 0, 1, 1) == sqrt(2)*hbar
|
||
|
|
assert Jminus.rewrite('xyz') == Jx - I*Jy
|
||
|
|
# Normal operators, normal states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jminus*JxKet(1, 1)) == \
|
||
|
|
hbar*sqrt(2)*JxKet(1, 0)/2 + hbar*JxKet(1, 1)
|
||
|
|
assert qapply(Jminus*JyKet(1, 1)) == \
|
||
|
|
hbar*sqrt(2)*JyKet(1, 0)/2 - hbar*I*JyKet(1, 1)
|
||
|
|
assert qapply(Jminus*JzKet(1, 1)) == sqrt(2)*hbar*JzKet(1, 0)
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jminus*JxKet(j, m)) == \
|
||
|
|
Sum(hbar*sqrt(j**2 + j - mi**2 + mi)*WignerD(j, mi, m, 0, pi/2, 0) *
|
||
|
|
Sum(WignerD(j, mi1, mi - 1, 0, pi*Rational(3, 2), 0)*JxKet(j, mi1),
|
||
|
|
(mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jminus*JyKet(j, m)) == \
|
||
|
|
Sum(hbar*sqrt(j**2 + j - mi**2 + mi)*WignerD(j, mi, m, pi*Rational(3, 2), -pi/2, pi/2) *
|
||
|
|
Sum(WignerD(j, mi1, mi - 1, pi*Rational(3, 2), pi/2, pi/2)*JyKet(j, mi1),
|
||
|
|
(mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jminus*JzKet(j, m)) == \
|
||
|
|
hbar*sqrt(j**2 + j - m**2 + m)*JzKet(j, m - 1)
|
||
|
|
# Normal operators, coupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jminus*JxKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
hbar*sqrt(2)*JxKetCoupled(1, 0, (1, 1))/2 + \
|
||
|
|
hbar*JxKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(Jminus*JyKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
hbar*sqrt(2)*JyKetCoupled(1, 0, (1, 1))/2 - \
|
||
|
|
hbar*I*JyKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(Jminus*JzKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
sqrt(2)*hbar*JzKetCoupled(1, 0, (1, 1))
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jminus*JxKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
Sum(hbar*sqrt(j**2 + j - mi**2 + mi)*WignerD(j, mi, m, 0, pi/2, 0) *
|
||
|
|
Sum(WignerD(j, mi1, mi - 1, 0, pi*Rational(3, 2), 0)*JxKetCoupled(j, mi1, (j1, j2)),
|
||
|
|
(mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jminus*JyKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
Sum(hbar*sqrt(j**2 + j - mi**2 + mi)*WignerD(j, mi, m, pi*Rational(3, 2), -pi/2, pi/2) *
|
||
|
|
Sum(
|
||
|
|
WignerD(j, mi1, mi - 1, pi*Rational(3, 2), pi/2, pi/2)*
|
||
|
|
JyKetCoupled(j, mi1, (j1, j2)),
|
||
|
|
(mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jminus*JzKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
hbar*sqrt(j**2 + j - m**2 + m)*JzKetCoupled(j, m - 1, (j1, j2))
|
||
|
|
# Uncoupled operators, uncoupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(TensorProduct(Jminus, 1)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JxKet(1, 0), JxKet(1, -1))/2 + \
|
||
|
|
hbar*TensorProduct(JxKet(1, 1), JxKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, Jminus)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
-hbar*TensorProduct(JxKet(1, 1), JxKet(1, -1)) - \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JxKet(1, 1), JxKet(1, 0))/2
|
||
|
|
assert qapply(TensorProduct(Jminus, 1)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JyKet(1, 0), JyKet(1, -1))/2 - \
|
||
|
|
hbar*I*TensorProduct(JyKet(1, 1), JyKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, Jminus)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
hbar*I*TensorProduct(JyKet(1, 1), JyKet(1, -1)) + \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JyKet(1, 1), JyKet(1, 0))/2
|
||
|
|
assert qapply(TensorProduct(Jminus, 1)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
sqrt(2)*hbar*TensorProduct(JzKet(1, 0), JzKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(
|
||
|
|
1, Jminus)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == 0
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(TensorProduct(Jminus, 1)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(Sum(hbar*sqrt(j1**2 + j1 - mi**2 + mi)*WignerD(j1, mi, m1, 0, pi/2, 0) *
|
||
|
|
Sum(WignerD(j1, mi1, mi - 1, 0, pi*Rational(3, 2), 0)*JxKet(j1, mi1),
|
||
|
|
(mi1, -j1, j1)), (mi, -j1, j1)), JxKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jminus)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(JxKet(j1, m1), Sum(hbar*sqrt(j2**2 + j2 - mi**2 + mi)*WignerD(j2, mi, m2, 0, pi/2, 0) *
|
||
|
|
Sum(WignerD(j2, mi1, mi - 1, 0, pi*Rational(3, 2), 0)*JxKet(j2, mi1),
|
||
|
|
(mi1, -j2, j2)), (mi, -j2, j2)))
|
||
|
|
assert qapply(TensorProduct(Jminus, 1)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(Sum(hbar*sqrt(j1**2 + j1 - mi**2 + mi)*WignerD(j1, mi, m1, pi*Rational(3, 2), -pi/2, pi/2) *
|
||
|
|
Sum(WignerD(j1, mi1, mi - 1, pi*Rational(3, 2), pi/2, pi/2)*JyKet(j1, mi1),
|
||
|
|
(mi1, -j1, j1)), (mi, -j1, j1)), JyKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jminus)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(JyKet(j1, m1), Sum(hbar*sqrt(j2**2 + j2 - mi**2 + mi)*WignerD(j2, mi, m2, pi*Rational(3, 2), -pi/2, pi/2) *
|
||
|
|
Sum(WignerD(j2, mi1, mi - 1, pi*Rational(3, 2), pi/2, pi/2)*JyKet(j2, mi1),
|
||
|
|
(mi1, -j2, j2)), (mi, -j2, j2)))
|
||
|
|
assert qapply(TensorProduct(Jminus, 1)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*sqrt(
|
||
|
|
j1**2 + j1 - m1**2 + m1)*TensorProduct(JzKet(j1, m1 - 1), JzKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jminus)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*sqrt(
|
||
|
|
j2**2 + j2 - m2**2 + m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 - 1))
|
||
|
|
|
||
|
|
|
||
|
|
def test_j2():
|
||
|
|
assert Commutator(J2, Jz).doit() == 0
|
||
|
|
assert J2.matrix_element(1, 1, 1, 1) == 2*hbar**2
|
||
|
|
# Normal operators, normal states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(J2*JxKet(1, 1)) == 2*hbar**2*JxKet(1, 1)
|
||
|
|
assert qapply(J2*JyKet(1, 1)) == 2*hbar**2*JyKet(1, 1)
|
||
|
|
assert qapply(J2*JzKet(1, 1)) == 2*hbar**2*JzKet(1, 1)
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(J2*JxKet(j, m)) == \
|
||
|
|
hbar**2*j**2*JxKet(j, m) + hbar**2*j*JxKet(j, m)
|
||
|
|
assert qapply(J2*JyKet(j, m)) == \
|
||
|
|
hbar**2*j**2*JyKet(j, m) + hbar**2*j*JyKet(j, m)
|
||
|
|
assert qapply(J2*JzKet(j, m)) == \
|
||
|
|
hbar**2*j**2*JzKet(j, m) + hbar**2*j*JzKet(j, m)
|
||
|
|
# Normal operators, coupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(J2*JxKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
2*hbar**2*JxKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(J2*JyKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
2*hbar**2*JyKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(J2*JzKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
2*hbar**2*JzKetCoupled(1, 1, (1, 1))
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(J2*JxKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
hbar**2*j**2*JxKetCoupled(j, m, (j1, j2)) + \
|
||
|
|
hbar**2*j*JxKetCoupled(j, m, (j1, j2))
|
||
|
|
assert qapply(J2*JyKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
hbar**2*j**2*JyKetCoupled(j, m, (j1, j2)) + \
|
||
|
|
hbar**2*j*JyKetCoupled(j, m, (j1, j2))
|
||
|
|
assert qapply(J2*JzKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
hbar**2*j**2*JzKetCoupled(j, m, (j1, j2)) + \
|
||
|
|
hbar**2*j*JzKetCoupled(j, m, (j1, j2))
|
||
|
|
# Uncoupled operators, uncoupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(TensorProduct(J2, 1)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
2*hbar**2*TensorProduct(JxKet(1, 1), JxKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, J2)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
2*hbar**2*TensorProduct(JxKet(1, 1), JxKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(J2, 1)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
2*hbar**2*TensorProduct(JyKet(1, 1), JyKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, J2)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
2*hbar**2*TensorProduct(JyKet(1, 1), JyKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(J2, 1)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
2*hbar**2*TensorProduct(JzKet(1, 1), JzKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, J2)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
2*hbar**2*TensorProduct(JzKet(1, 1), JzKet(1, -1))
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(TensorProduct(J2, 1)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
hbar**2*j1**2*TensorProduct(JxKet(j1, m1), JxKet(j2, m2)) + \
|
||
|
|
hbar**2*j1*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, J2)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
hbar**2*j2**2*TensorProduct(JxKet(j1, m1), JxKet(j2, m2)) + \
|
||
|
|
hbar**2*j2*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(J2, 1)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
hbar**2*j1**2*TensorProduct(JyKet(j1, m1), JyKet(j2, m2)) + \
|
||
|
|
hbar**2*j1*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, J2)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
hbar**2*j2**2*TensorProduct(JyKet(j1, m1), JyKet(j2, m2)) + \
|
||
|
|
hbar**2*j2*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(J2, 1)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar**2*j1**2*TensorProduct(JzKet(j1, m1), JzKet(j2, m2)) + \
|
||
|
|
hbar**2*j1*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, J2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar**2*j2**2*TensorProduct(JzKet(j1, m1), JzKet(j2, m2)) + \
|
||
|
|
hbar**2*j2*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))
|
||
|
|
|
||
|
|
|
||
|
|
def test_jx():
|
||
|
|
assert Commutator(Jx, Jz).doit() == -I*hbar*Jy
|
||
|
|
assert Jx.rewrite('plusminus') == (Jminus + Jplus)/2
|
||
|
|
assert represent(Jx, basis=Jz, j=1) == (
|
||
|
|
represent(Jplus, basis=Jz, j=1) + represent(Jminus, basis=Jz, j=1))/2
|
||
|
|
# Normal operators, normal states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jx*JxKet(1, 1)) == hbar*JxKet(1, 1)
|
||
|
|
assert qapply(Jx*JyKet(1, 1)) == hbar*JyKet(1, 1)
|
||
|
|
assert qapply(Jx*JzKet(1, 1)) == sqrt(2)*hbar*JzKet(1, 0)/2
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jx*JxKet(j, m)) == hbar*m*JxKet(j, m)
|
||
|
|
assert qapply(Jx*JyKet(j, m)) == \
|
||
|
|
Sum(hbar*mi*WignerD(j, mi, m, 0, 0, pi/2)*Sum(WignerD(j,
|
||
|
|
mi1, mi, pi*Rational(3, 2), 0, 0)*JyKet(j, mi1), (mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jx*JzKet(j, m)) == \
|
||
|
|
hbar*sqrt(j**2 + j - m**2 - m)*JzKet(j, m + 1)/2 + hbar*sqrt(j**2 +
|
||
|
|
j - m**2 + m)*JzKet(j, m - 1)/2
|
||
|
|
# Normal operators, coupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jx*JxKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
hbar*JxKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(Jx*JyKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
hbar*JyKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(Jx*JzKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
sqrt(2)*hbar*JzKetCoupled(1, 0, (1, 1))/2
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jx*JxKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
hbar*m*JxKetCoupled(j, m, (j1, j2))
|
||
|
|
assert qapply(Jx*JyKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
Sum(hbar*mi*WignerD(j, mi, m, 0, 0, pi/2)*Sum(WignerD(j, mi1, mi, pi*Rational(3, 2), 0, 0)*JyKetCoupled(j, mi1, (j1, j2)), (mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jx*JzKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
hbar*sqrt(j**2 + j - m**2 - m)*JzKetCoupled(j, m + 1, (j1, j2))/2 + \
|
||
|
|
hbar*sqrt(j**2 + j - m**2 + m)*JzKetCoupled(j, m - 1, (j1, j2))/2
|
||
|
|
# Normal operators, uncoupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jx*TensorProduct(JxKet(1, 1), JxKet(1, 1))) == \
|
||
|
|
2*hbar*TensorProduct(JxKet(1, 1), JxKet(1, 1))
|
||
|
|
assert qapply(Jx*TensorProduct(JyKet(1, 1), JyKet(1, 1))) == \
|
||
|
|
hbar*TensorProduct(JyKet(1, 1), JyKet(1, 1)) + \
|
||
|
|
hbar*TensorProduct(JyKet(1, 1), JyKet(1, 1))
|
||
|
|
assert qapply(Jx*TensorProduct(JzKet(1, 1), JzKet(1, 1))) == \
|
||
|
|
sqrt(2)*hbar*TensorProduct(JzKet(1, 1), JzKet(1, 0))/2 + \
|
||
|
|
sqrt(2)*hbar*TensorProduct(JzKet(1, 0), JzKet(1, 1))/2
|
||
|
|
assert qapply(Jx*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == 0
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jx*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
hbar*m1*TensorProduct(JxKet(j1, m1), JxKet(j2, m2)) + \
|
||
|
|
hbar*m2*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))
|
||
|
|
assert qapply(Jx*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(Sum(hbar*mi*WignerD(j1, mi, m1, 0, 0, pi/2)*Sum(WignerD(j1, mi1, mi, pi*Rational(3, 2), 0, 0)*JyKet(j1, mi1), (mi1, -j1, j1)), (mi, -j1, j1)), JyKet(j2, m2)) + \
|
||
|
|
TensorProduct(JyKet(j1, m1), Sum(hbar*mi*WignerD(j2, mi, m2, 0, 0, pi/2)*Sum(WignerD(j2, mi1, mi, pi*Rational(3, 2), 0, 0)*JyKet(j2, mi1), (mi1, -j2, j2)), (mi, -j2, j2)))
|
||
|
|
assert qapply(Jx*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*sqrt(j1**2 + j1 - m1**2 - m1)*TensorProduct(JzKet(j1, m1 + 1), JzKet(j2, m2))/2 + \
|
||
|
|
hbar*sqrt(j1**2 + j1 - m1**2 + m1)*TensorProduct(JzKet(j1, m1 - 1), JzKet(j2, m2))/2 + \
|
||
|
|
hbar*sqrt(j2**2 + j2 - m2**2 - m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 + 1))/2 + \
|
||
|
|
hbar*sqrt(
|
||
|
|
j2**2 + j2 - m2**2 + m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 - 1))/2
|
||
|
|
# Uncoupled operators, uncoupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(TensorProduct(Jx, 1)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
hbar*TensorProduct(JxKet(1, 1), JxKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, Jx)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
-hbar*TensorProduct(JxKet(1, 1), JxKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(Jx, 1)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
hbar*TensorProduct(JyKet(1, 1), JyKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, Jx)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
-hbar*TensorProduct(JyKet(1, 1), JyKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(Jx, 1)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JzKet(1, 0), JzKet(1, -1))/2
|
||
|
|
assert qapply(TensorProduct(1, Jx)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
hbar*sqrt(2)*TensorProduct(JzKet(1, 1), JzKet(1, 0))/2
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(TensorProduct(Jx, 1)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
hbar*m1*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jx)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
hbar*m2*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(Jx, 1)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(Sum(hbar*mi*WignerD(j1, mi, m1, 0, 0, pi/2) * Sum(WignerD(j1, mi1, mi, pi*Rational(3, 2), 0, 0)*JyKet(j1, mi1), (mi1, -j1, j1)), (mi, -j1, j1)), JyKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jx)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(JyKet(j1, m1), Sum(hbar*mi*WignerD(j2, mi, m2, 0, 0, pi/2) * Sum(WignerD(j2, mi1, mi, pi*Rational(3, 2), 0, 0)*JyKet(j2, mi1), (mi1, -j2, j2)), (mi, -j2, j2)))
|
||
|
|
assert qapply(TensorProduct(Jx, 1)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*sqrt(j1**2 + j1 - m1**2 - m1)*TensorProduct(JzKet(j1, m1 + 1), JzKet(j2, m2))/2 + \
|
||
|
|
hbar*sqrt(
|
||
|
|
j1**2 + j1 - m1**2 + m1)*TensorProduct(JzKet(j1, m1 - 1), JzKet(j2, m2))/2
|
||
|
|
assert qapply(TensorProduct(1, Jx)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*sqrt(j2**2 + j2 - m2**2 - m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 + 1))/2 + \
|
||
|
|
hbar*sqrt(
|
||
|
|
j2**2 + j2 - m2**2 + m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 - 1))/2
|
||
|
|
|
||
|
|
|
||
|
|
def test_jy():
|
||
|
|
assert Commutator(Jy, Jz).doit() == I*hbar*Jx
|
||
|
|
assert Jy.rewrite('plusminus') == (Jplus - Jminus)/(2*I)
|
||
|
|
assert represent(Jy, basis=Jz) == (
|
||
|
|
represent(Jplus, basis=Jz) - represent(Jminus, basis=Jz))/(2*I)
|
||
|
|
# Normal operators, normal states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jy*JxKet(1, 1)) == hbar*JxKet(1, 1)
|
||
|
|
assert qapply(Jy*JyKet(1, 1)) == hbar*JyKet(1, 1)
|
||
|
|
assert qapply(Jy*JzKet(1, 1)) == sqrt(2)*hbar*I*JzKet(1, 0)/2
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jy*JxKet(j, m)) == \
|
||
|
|
Sum(hbar*mi*WignerD(j, mi, m, pi*Rational(3, 2), 0, 0)*Sum(WignerD(
|
||
|
|
j, mi1, mi, 0, 0, pi/2)*JxKet(j, mi1), (mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jy*JyKet(j, m)) == hbar*m*JyKet(j, m)
|
||
|
|
assert qapply(Jy*JzKet(j, m)) == \
|
||
|
|
-hbar*I*sqrt(j**2 + j - m**2 - m)*JzKet(
|
||
|
|
j, m + 1)/2 + hbar*I*sqrt(j**2 + j - m**2 + m)*JzKet(j, m - 1)/2
|
||
|
|
# Normal operators, coupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jy*JxKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
hbar*JxKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(Jy*JyKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
hbar*JyKetCoupled(1, 1, (1, 1))
|
||
|
|
assert qapply(Jy*JzKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
sqrt(2)*hbar*I*JzKetCoupled(1, 0, (1, 1))/2
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jy*JxKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
Sum(hbar*mi*WignerD(j, mi, m, pi*Rational(3, 2), 0, 0)*Sum(WignerD(j, mi1, mi, 0, 0, pi/2)*JxKetCoupled(j, mi1, (j1, j2)), (mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jy*JyKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
hbar*m*JyKetCoupled(j, m, (j1, j2))
|
||
|
|
assert qapply(Jy*JzKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
-hbar*I*sqrt(j**2 + j - m**2 - m)*JzKetCoupled(j, m + 1, (j1, j2))/2 + \
|
||
|
|
hbar*I*sqrt(j**2 + j - m**2 + m)*JzKetCoupled(j, m - 1, (j1, j2))/2
|
||
|
|
# Normal operators, uncoupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jy*TensorProduct(JxKet(1, 1), JxKet(1, 1))) == \
|
||
|
|
hbar*TensorProduct(JxKet(1, 1), JxKet(1, 1)) + \
|
||
|
|
hbar*TensorProduct(JxKet(1, 1), JxKet(1, 1))
|
||
|
|
assert qapply(Jy*TensorProduct(JyKet(1, 1), JyKet(1, 1))) == \
|
||
|
|
2*hbar*TensorProduct(JyKet(1, 1), JyKet(1, 1))
|
||
|
|
assert qapply(Jy*TensorProduct(JzKet(1, 1), JzKet(1, 1))) == \
|
||
|
|
sqrt(2)*hbar*I*TensorProduct(JzKet(1, 1), JzKet(1, 0))/2 + \
|
||
|
|
sqrt(2)*hbar*I*TensorProduct(JzKet(1, 0), JzKet(1, 1))/2
|
||
|
|
assert qapply(Jy*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == 0
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jy*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(JxKet(j1, m1), Sum(hbar*mi*WignerD(j2, mi, m2, pi*Rational(3, 2), 0, 0)*Sum(WignerD(j2, mi1, mi, 0, 0, pi/2)*JxKet(j2, mi1), (mi1, -j2, j2)), (mi, -j2, j2))) + \
|
||
|
|
TensorProduct(Sum(hbar*mi*WignerD(j1, mi, m1, pi*Rational(3, 2), 0, 0)*Sum(WignerD(j1, mi1, mi, 0, 0, pi/2)*JxKet(j1, mi1), (mi1, -j1, j1)), (mi, -j1, j1)), JxKet(j2, m2))
|
||
|
|
assert qapply(Jy*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
hbar*m1*TensorProduct(JyKet(j1, m1), JyKet(
|
||
|
|
j2, m2)) + hbar*m2*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))
|
||
|
|
assert qapply(Jy*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
-hbar*I*sqrt(j1**2 + j1 - m1**2 - m1)*TensorProduct(JzKet(j1, m1 + 1), JzKet(j2, m2))/2 + \
|
||
|
|
hbar*I*sqrt(j1**2 + j1 - m1**2 + m1)*TensorProduct(JzKet(j1, m1 - 1), JzKet(j2, m2))/2 + \
|
||
|
|
-hbar*I*sqrt(j2**2 + j2 - m2**2 - m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 + 1))/2 + \
|
||
|
|
hbar*I*sqrt(
|
||
|
|
j2**2 + j2 - m2**2 + m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 - 1))/2
|
||
|
|
# Uncoupled operators, uncoupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(TensorProduct(Jy, 1)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
hbar*TensorProduct(JxKet(1, 1), JxKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, Jy)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
-hbar*TensorProduct(JxKet(1, 1), JxKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(Jy, 1)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
hbar*TensorProduct(JyKet(1, 1), JyKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, Jy)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
-hbar*TensorProduct(JyKet(1, 1), JyKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(Jy, 1)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
hbar*sqrt(2)*I*TensorProduct(JzKet(1, 0), JzKet(1, -1))/2
|
||
|
|
assert qapply(TensorProduct(1, Jy)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
-hbar*sqrt(2)*I*TensorProduct(JzKet(1, 1), JzKet(1, 0))/2
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(TensorProduct(Jy, 1)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(Sum(hbar*mi*WignerD(j1, mi, m1, pi*Rational(3, 2), 0, 0) * Sum(WignerD(j1, mi1, mi, 0, 0, pi/2)*JxKet(j1, mi1), (mi1, -j1, j1)), (mi, -j1, j1)), JxKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jy)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(JxKet(j1, m1), Sum(hbar*mi*WignerD(j2, mi, m2, pi*Rational(3, 2), 0, 0) * Sum(WignerD(j2, mi1, mi, 0, 0, pi/2)*JxKet(j2, mi1), (mi1, -j2, j2)), (mi, -j2, j2)))
|
||
|
|
assert qapply(TensorProduct(Jy, 1)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
hbar*m1*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jy)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
hbar*m2*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(Jy, 1)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
-hbar*I*sqrt(j1**2 + j1 - m1**2 - m1)*TensorProduct(JzKet(j1, m1 + 1), JzKet(j2, m2))/2 + \
|
||
|
|
hbar*I*sqrt(
|
||
|
|
j1**2 + j1 - m1**2 + m1)*TensorProduct(JzKet(j1, m1 - 1), JzKet(j2, m2))/2
|
||
|
|
assert qapply(TensorProduct(1, Jy)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
-hbar*I*sqrt(j2**2 + j2 - m2**2 - m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 + 1))/2 + \
|
||
|
|
hbar*I*sqrt(
|
||
|
|
j2**2 + j2 - m2**2 + m2)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2 - 1))/2
|
||
|
|
|
||
|
|
|
||
|
|
def test_jz():
|
||
|
|
assert Commutator(Jz, Jminus).doit() == -hbar*Jminus
|
||
|
|
# Normal operators, normal states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jz*JxKet(1, 1)) == -sqrt(2)*hbar*JxKet(1, 0)/2
|
||
|
|
assert qapply(Jz*JyKet(1, 1)) == -sqrt(2)*hbar*I*JyKet(1, 0)/2
|
||
|
|
assert qapply(Jz*JzKet(2, 1)) == hbar*JzKet(2, 1)
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jz*JxKet(j, m)) == \
|
||
|
|
Sum(hbar*mi*WignerD(j, mi, m, 0, pi/2, 0)*Sum(WignerD(j,
|
||
|
|
mi1, mi, 0, pi*Rational(3, 2), 0)*JxKet(j, mi1), (mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jz*JyKet(j, m)) == \
|
||
|
|
Sum(hbar*mi*WignerD(j, mi, m, pi*Rational(3, 2), -pi/2, pi/2)*Sum(WignerD(j, mi1,
|
||
|
|
mi, pi*Rational(3, 2), pi/2, pi/2)*JyKet(j, mi1), (mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jz*JzKet(j, m)) == hbar*m*JzKet(j, m)
|
||
|
|
# Normal operators, coupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jz*JxKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
-sqrt(2)*hbar*JxKetCoupled(1, 0, (1, 1))/2
|
||
|
|
assert qapply(Jz*JyKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
-sqrt(2)*hbar*I*JyKetCoupled(1, 0, (1, 1))/2
|
||
|
|
assert qapply(Jz*JzKetCoupled(1, 1, (1, 1))) == \
|
||
|
|
hbar*JzKetCoupled(1, 1, (1, 1))
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jz*JxKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
Sum(hbar*mi*WignerD(j, mi, m, 0, pi/2, 0)*Sum(WignerD(j, mi1, mi, 0, pi*Rational(3, 2), 0)*JxKetCoupled(j, mi1, (j1, j2)), (mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jz*JyKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
Sum(hbar*mi*WignerD(j, mi, m, pi*Rational(3, 2), -pi/2, pi/2)*Sum(WignerD(j, mi1, mi, pi*Rational(3, 2), pi/2, pi/2)*JyKetCoupled(j, mi1, (j1, j2)), (mi1, -j, j)), (mi, -j, j))
|
||
|
|
assert qapply(Jz*JzKetCoupled(j, m, (j1, j2))) == \
|
||
|
|
hbar*m*JzKetCoupled(j, m, (j1, j2))
|
||
|
|
# Normal operators, uncoupled states
|
||
|
|
# Numerical
|
||
|
|
assert qapply(Jz*TensorProduct(JxKet(1, 1), JxKet(1, 1))) == \
|
||
|
|
-sqrt(2)*hbar*TensorProduct(JxKet(1, 1), JxKet(1, 0))/2 - \
|
||
|
|
sqrt(2)*hbar*TensorProduct(JxKet(1, 0), JxKet(1, 1))/2
|
||
|
|
assert qapply(Jz*TensorProduct(JyKet(1, 1), JyKet(1, 1))) == \
|
||
|
|
-sqrt(2)*hbar*I*TensorProduct(JyKet(1, 1), JyKet(1, 0))/2 - \
|
||
|
|
sqrt(2)*hbar*I*TensorProduct(JyKet(1, 0), JyKet(1, 1))/2
|
||
|
|
assert qapply(Jz*TensorProduct(JzKet(1, 1), JzKet(1, 1))) == \
|
||
|
|
2*hbar*TensorProduct(JzKet(1, 1), JzKet(1, 1))
|
||
|
|
assert qapply(Jz*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == 0
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(Jz*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(JxKet(j1, m1), Sum(hbar*mi*WignerD(j2, mi, m2, 0, pi/2, 0)*Sum(WignerD(j2, mi1, mi, 0, pi*Rational(3, 2), 0)*JxKet(j2, mi1), (mi1, -j2, j2)), (mi, -j2, j2))) + \
|
||
|
|
TensorProduct(Sum(hbar*mi*WignerD(j1, mi, m1, 0, pi/2, 0)*Sum(WignerD(j1, mi1, mi, 0, pi*Rational(3, 2), 0)*JxKet(j1, mi1), (mi1, -j1, j1)), (mi, -j1, j1)), JxKet(j2, m2))
|
||
|
|
assert qapply(Jz*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(JyKet(j1, m1), Sum(hbar*mi*WignerD(j2, mi, m2, pi*Rational(3, 2), -pi/2, pi/2)*Sum(WignerD(j2, mi1, mi, pi*Rational(3, 2), pi/2, pi/2)*JyKet(j2, mi1), (mi1, -j2, j2)), (mi, -j2, j2))) + \
|
||
|
|
TensorProduct(Sum(hbar*mi*WignerD(j1, mi, m1, pi*Rational(3, 2), -pi/2, pi/2)*Sum(WignerD(j1, mi1, mi, pi*Rational(3, 2), pi/2, pi/2)*JyKet(j1, mi1), (mi1, -j1, j1)), (mi, -j1, j1)), JyKet(j2, m2))
|
||
|
|
assert qapply(Jz*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*m1*TensorProduct(JzKet(j1, m1), JzKet(
|
||
|
|
j2, m2)) + hbar*m2*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))
|
||
|
|
# Uncoupled Operators
|
||
|
|
# Numerical
|
||
|
|
assert qapply(TensorProduct(Jz, 1)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
-sqrt(2)*hbar*TensorProduct(JxKet(1, 0), JxKet(1, -1))/2
|
||
|
|
assert qapply(TensorProduct(1, Jz)*TensorProduct(JxKet(1, 1), JxKet(1, -1))) == \
|
||
|
|
-sqrt(2)*hbar*TensorProduct(JxKet(1, 1), JxKet(1, 0))/2
|
||
|
|
assert qapply(TensorProduct(Jz, 1)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
-sqrt(2)*I*hbar*TensorProduct(JyKet(1, 0), JyKet(1, -1))/2
|
||
|
|
assert qapply(TensorProduct(1, Jz)*TensorProduct(JyKet(1, 1), JyKet(1, -1))) == \
|
||
|
|
sqrt(2)*I*hbar*TensorProduct(JyKet(1, 1), JyKet(1, 0))/2
|
||
|
|
assert qapply(TensorProduct(Jz, 1)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
hbar*TensorProduct(JzKet(1, 1), JzKet(1, -1))
|
||
|
|
assert qapply(TensorProduct(1, Jz)*TensorProduct(JzKet(1, 1), JzKet(1, -1))) == \
|
||
|
|
-hbar*TensorProduct(JzKet(1, 1), JzKet(1, -1))
|
||
|
|
# Symbolic
|
||
|
|
assert qapply(TensorProduct(Jz, 1)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(Sum(hbar*mi*WignerD(j1, mi, m1, 0, pi/2, 0)*Sum(WignerD(j1, mi1, mi, 0, pi*Rational(3, 2), 0)*JxKet(j1, mi1), (mi1, -j1, j1)), (mi, -j1, j1)), JxKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jz)*TensorProduct(JxKet(j1, m1), JxKet(j2, m2))) == \
|
||
|
|
TensorProduct(JxKet(j1, m1), Sum(hbar*mi*WignerD(j2, mi, m2, 0, pi/2, 0)*Sum(WignerD(j2, mi1, mi, 0, pi*Rational(3, 2), 0)*JxKet(j2, mi1), (mi1, -j2, j2)), (mi, -j2, j2)))
|
||
|
|
assert qapply(TensorProduct(Jz, 1)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(Sum(hbar*mi*WignerD(j1, mi, m1, pi*Rational(3, 2), -pi/2, pi/2)*Sum(WignerD(j1, mi1, mi, pi*Rational(3, 2), pi/2, pi/2)*JyKet(j1, mi1), (mi1, -j1, j1)), (mi, -j1, j1)), JyKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jz)*TensorProduct(JyKet(j1, m1), JyKet(j2, m2))) == \
|
||
|
|
TensorProduct(JyKet(j1, m1), Sum(hbar*mi*WignerD(j2, mi, m2, pi*Rational(3, 2), -pi/2, pi/2)*Sum(WignerD(j2, mi1, mi, pi*Rational(3, 2), pi/2, pi/2)*JyKet(j2, mi1), (mi1, -j2, j2)), (mi, -j2, j2)))
|
||
|
|
assert qapply(TensorProduct(Jz, 1)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*m1*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))
|
||
|
|
assert qapply(TensorProduct(1, Jz)*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))) == \
|
||
|
|
hbar*m2*TensorProduct(JzKet(j1, m1), JzKet(j2, m2))
|
||
|
|
|
||
|
|
|
||
|
|
def test_rotation():
|
||
|
|
a, b, g = symbols('a b g')
|
||
|
|
j, m = symbols('j m')
|
||
|
|
#Uncoupled
|
||
|
|
answ = [JxKet(1,-1)/2 - sqrt(2)*JxKet(1,0)/2 + JxKet(1,1)/2 ,
|
||
|
|
JyKet(1,-1)/2 - sqrt(2)*JyKet(1,0)/2 + JyKet(1,1)/2 ,
|
||
|
|
JzKet(1,-1)/2 - sqrt(2)*JzKet(1,0)/2 + JzKet(1,1)/2]
|
||
|
|
fun = [state(1, 1) for state in (JxKet, JyKet, JzKet)]
|
||
|
|
for state in fun:
|
||
|
|
got = qapply(Rotation(0, pi/2, 0)*state)
|
||
|
|
assert got in answ
|
||
|
|
answ.remove(got)
|
||
|
|
assert not answ
|
||
|
|
arg = Rotation(a, b, g)*fun[0]
|
||
|
|
assert qapply(arg) == (-exp(-I*a)*exp(I*g)*cos(b)*JxKet(1,-1)/2 +
|
||
|
|
exp(-I*a)*exp(I*g)*JxKet(1,-1)/2 - sqrt(2)*exp(-I*a)*sin(b)*JxKet(1,0)/2 +
|
||
|
|
exp(-I*a)*exp(-I*g)*cos(b)*JxKet(1,1)/2 + exp(-I*a)*exp(-I*g)*JxKet(1,1)/2)
|
||
|
|
#dummy effective
|
||
|
|
assert str(qapply(Rotation(a, b, g)*JzKet(j, m), dummy=False)) == str(
|
||
|
|
qapply(Rotation(a, b, g)*JzKet(j, m), dummy=True)).replace('_','')
|
||
|
|
#Coupled
|
||
|
|
ans = [JxKetCoupled(1,-1,(1,1))/2 - sqrt(2)*JxKetCoupled(1,0,(1,1))/2 +
|
||
|
|
JxKetCoupled(1,1,(1,1))/2 ,
|
||
|
|
JyKetCoupled(1,-1,(1,1))/2 - sqrt(2)*JyKetCoupled(1,0,(1,1))/2 +
|
||
|
|
JyKetCoupled(1,1,(1,1))/2 ,
|
||
|
|
JzKetCoupled(1,-1,(1,1))/2 - sqrt(2)*JzKetCoupled(1,0,(1,1))/2 +
|
||
|
|
JzKetCoupled(1,1,(1,1))/2]
|
||
|
|
fun = [state(1, 1, (1,1)) for state in (JxKetCoupled, JyKetCoupled, JzKetCoupled)]
|
||
|
|
for state in fun:
|
||
|
|
got = qapply(Rotation(0, pi/2, 0)*state)
|
||
|
|
assert got in ans
|
||
|
|
ans.remove(got)
|
||
|
|
assert not ans
|
||
|
|
arg = Rotation(a, b, g)*fun[0]
|
||
|
|
assert qapply(arg) == (
|
||
|
|
-exp(-I*a)*exp(I*g)*cos(b)*JxKetCoupled(1,-1,(1,1))/2 +
|
||
|
|
exp(-I*a)*exp(I*g)*JxKetCoupled(1,-1,(1,1))/2 -
|
||
|
|
sqrt(2)*exp(-I*a)*sin(b)*JxKetCoupled(1,0,(1,1))/2 +
|
||
|
|
exp(-I*a)*exp(-I*g)*cos(b)*JxKetCoupled(1,1,(1,1))/2 +
|
||
|
|
exp(-I*a)*exp(-I*g)*JxKetCoupled(1,1,(1,1))/2)
|
||
|
|
#dummy effective
|
||
|
|
assert str(qapply(Rotation(a,b,g)*JzKetCoupled(j,m,(j1,j2)), dummy=False)) == str(
|
||
|
|
qapply(Rotation(a,b,g)*JzKetCoupled(j,m,(j1,j2)), dummy=True)).replace('_','')
|
||
|
|
|
||
|
|
|
||
|
|
def test_jzket():
|
||
|
|
j, m = symbols('j m')
|
||
|
|
# j not integer or half integer
|
||
|
|
raises(ValueError, lambda: JzKet(Rational(2, 3), Rational(-1, 3)))
|
||
|
|
raises(ValueError, lambda: JzKet(Rational(2, 3), m))
|
||
|
|
# j < 0
|
||
|
|
raises(ValueError, lambda: JzKet(-1, 1))
|
||
|
|
raises(ValueError, lambda: JzKet(-1, m))
|
||
|
|
# m not integer or half integer
|
||
|
|
raises(ValueError, lambda: JzKet(j, Rational(-1, 3)))
|
||
|
|
# abs(m) > j
|
||
|
|
raises(ValueError, lambda: JzKet(1, 2))
|
||
|
|
raises(ValueError, lambda: JzKet(1, -2))
|
||
|
|
# j-m not integer
|
||
|
|
raises(ValueError, lambda: JzKet(1, S.Half))
|
||
|
|
|
||
|
|
|
||
|
|
def test_jzketcoupled():
|
||
|
|
j, m = symbols('j m')
|
||
|
|
# j not integer or half integer
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(Rational(2, 3), Rational(-1, 3), (1,)))
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(Rational(2, 3), m, (1,)))
|
||
|
|
# j < 0
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(-1, 1, (1,)))
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(-1, m, (1,)))
|
||
|
|
# m not integer or half integer
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(j, Rational(-1, 3), (1,)))
|
||
|
|
# abs(m) > j
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 2, (1,)))
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, -2, (1,)))
|
||
|
|
# j-m not integer
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, S.Half, (1,)))
|
||
|
|
# checks types on coupling scheme
|
||
|
|
raises(TypeError, lambda: JzKetCoupled(1, 1, 1))
|
||
|
|
raises(TypeError, lambda: JzKetCoupled(1, 1, (1,), 1))
|
||
|
|
raises(TypeError, lambda: JzKetCoupled(1, 1, (1, 1), (1,)))
|
||
|
|
raises(TypeError, lambda: JzKetCoupled(1, 1, (1, 1, 1), (1, 2, 1),
|
||
|
|
(1, 3, 1)))
|
||
|
|
# checks length of coupling terms
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (1,), ((1, 2, 1),)))
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 1), ((1, 2),)))
|
||
|
|
# all jn are integer or half-integer
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (Rational(1, 3), Rational(2, 3))))
|
||
|
|
# indices in coupling scheme must be integers
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 1), ((S.Half, 1, 2),) ))
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 1), ((1, S.Half, 2),) ))
|
||
|
|
# indices out of range
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 1), ((0, 2, 1),) ))
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 1), ((3, 2, 1),) ))
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 1), ((1, 0, 1),) ))
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 1), ((1, 3, 1),) ))
|
||
|
|
# all j values in coupling scheme must by integer or half-integer
|
||
|
|
raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 1, 1), ((1, 2, S(
|
||
|
|
4)/3), (1, 3, 1)) ))
|
||
|
|
# each coupling must satisfy |j1-j2| <= j3 <= j1+j2
|
||
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raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 5)))
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raises(ValueError, lambda: JzKetCoupled(5, 1, (1, 1)))
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# final j of coupling must be j of the state
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raises(ValueError, lambda: JzKetCoupled(1, 1, (1, 1), ((1, 2, 2),) ))
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