105 lines
4.0 KiB
Python
105 lines
4.0 KiB
Python
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"""Tests for cartesian.py"""
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from sympy.core.numbers import (I, 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.special.delta_functions import DiracDelta
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from sympy.sets.sets import Interval
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from sympy.physics.quantum import qapply, represent, L2, Dagger
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from sympy.physics.quantum import Commutator, hbar
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from sympy.physics.quantum.cartesian import (
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XOp, YOp, ZOp, PxOp, X, Y, Z, Px, XKet, XBra, PxKet, PxBra,
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PositionKet3D, PositionBra3D
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)
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from sympy.physics.quantum.operator import DifferentialOperator
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x, y, z, x_1, x_2, x_3, y_1, z_1 = symbols('x,y,z,x_1,x_2,x_3,y_1,z_1')
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px, py, px_1, px_2 = symbols('px py px_1 px_2')
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def test_x():
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assert X.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
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assert Commutator(X, Px).doit() == I*hbar
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assert qapply(X*XKet(x)) == x*XKet(x)
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assert XKet(x).dual_class() == XBra
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assert XBra(x).dual_class() == XKet
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assert (Dagger(XKet(y))*XKet(x)).doit() == DiracDelta(x - y)
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assert (PxBra(px)*XKet(x)).doit() == \
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exp(-I*x*px/hbar)/sqrt(2*pi*hbar)
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assert represent(XKet(x)) == DiracDelta(x - x_1)
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assert represent(XBra(x)) == DiracDelta(-x + x_1)
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assert XBra(x).position == x
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assert represent(XOp()*XKet()) == x*DiracDelta(x - x_2)
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assert represent(XOp()*XKet()*XBra('y')) == \
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x*DiracDelta(x - x_3)*DiracDelta(x_1 - y)
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assert represent(XBra("y")*XKet()) == DiracDelta(x - y)
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assert represent(
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XKet()*XBra()) == DiracDelta(x - x_2) * DiracDelta(x_1 - x)
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rep_p = represent(XOp(), basis=PxOp)
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assert rep_p == hbar*I*DiracDelta(px_1 - px_2)*DifferentialOperator(px_1)
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assert rep_p == represent(XOp(), basis=PxOp())
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assert rep_p == represent(XOp(), basis=PxKet)
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assert rep_p == represent(XOp(), basis=PxKet())
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assert represent(XOp()*PxKet(), basis=PxKet) == \
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hbar*I*DiracDelta(px - px_2)*DifferentialOperator(px)
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def test_p():
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assert Px.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
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assert qapply(Px*PxKet(px)) == px*PxKet(px)
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assert PxKet(px).dual_class() == PxBra
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assert PxBra(x).dual_class() == PxKet
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assert (Dagger(PxKet(py))*PxKet(px)).doit() == DiracDelta(px - py)
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assert (XBra(x)*PxKet(px)).doit() == \
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exp(I*x*px/hbar)/sqrt(2*pi*hbar)
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assert represent(PxKet(px)) == DiracDelta(px - px_1)
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rep_x = represent(PxOp(), basis=XOp)
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assert rep_x == -hbar*I*DiracDelta(x_1 - x_2)*DifferentialOperator(x_1)
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assert rep_x == represent(PxOp(), basis=XOp())
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assert rep_x == represent(PxOp(), basis=XKet)
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assert rep_x == represent(PxOp(), basis=XKet())
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assert represent(PxOp()*XKet(), basis=XKet) == \
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-hbar*I*DiracDelta(x - x_2)*DifferentialOperator(x)
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assert represent(XBra("y")*PxOp()*XKet(), basis=XKet) == \
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-hbar*I*DiracDelta(x - y)*DifferentialOperator(x)
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def test_3dpos():
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assert Y.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
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assert Z.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
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test_ket = PositionKet3D(x, y, z)
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assert qapply(X*test_ket) == x*test_ket
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assert qapply(Y*test_ket) == y*test_ket
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assert qapply(Z*test_ket) == z*test_ket
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assert qapply(X*Y*test_ket) == x*y*test_ket
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assert qapply(X*Y*Z*test_ket) == x*y*z*test_ket
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assert qapply(Y*Z*test_ket) == y*z*test_ket
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assert PositionKet3D() == test_ket
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assert YOp() == Y
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assert ZOp() == Z
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assert PositionKet3D.dual_class() == PositionBra3D
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assert PositionBra3D.dual_class() == PositionKet3D
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other_ket = PositionKet3D(x_1, y_1, z_1)
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assert (Dagger(other_ket)*test_ket).doit() == \
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DiracDelta(x - x_1)*DiracDelta(y - y_1)*DiracDelta(z - z_1)
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assert test_ket.position_x == x
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assert test_ket.position_y == y
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assert test_ket.position_z == z
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assert other_ket.position_x == x_1
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assert other_ket.position_y == y_1
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assert other_ket.position_z == z_1
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# TODO: Add tests for representations
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