51 lines
1.6 KiB
Python
51 lines
1.6 KiB
Python
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from math import prod
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from sympy.core.numbers import Rational
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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.physics.quantum import Dagger, Commutator, qapply
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from sympy.physics.quantum.boson import BosonOp
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from sympy.physics.quantum.boson import (
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BosonFockKet, BosonFockBra, BosonCoherentKet, BosonCoherentBra)
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def test_bosonoperator():
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a = BosonOp('a')
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b = BosonOp('b')
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assert isinstance(a, BosonOp)
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assert isinstance(Dagger(a), BosonOp)
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assert a.is_annihilation
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assert not Dagger(a).is_annihilation
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assert BosonOp("a") == BosonOp("a", True)
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assert BosonOp("a") != BosonOp("c")
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assert BosonOp("a", True) != BosonOp("a", False)
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assert Commutator(a, Dagger(a)).doit() == 1
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assert Commutator(a, Dagger(b)).doit() == a * Dagger(b) - Dagger(b) * a
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assert Dagger(exp(a)) == exp(Dagger(a))
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def test_boson_states():
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a = BosonOp("a")
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# Fock states
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n = 3
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assert (BosonFockBra(0) * BosonFockKet(1)).doit() == 0
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assert (BosonFockBra(1) * BosonFockKet(1)).doit() == 1
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assert qapply(BosonFockBra(n) * Dagger(a)**n * BosonFockKet(0)) \
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== sqrt(prod(range(1, n+1)))
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# Coherent states
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alpha1, alpha2 = 1.2, 4.3
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assert (BosonCoherentBra(alpha1) * BosonCoherentKet(alpha1)).doit() == 1
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assert (BosonCoherentBra(alpha2) * BosonCoherentKet(alpha2)).doit() == 1
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assert abs((BosonCoherentBra(alpha1) * BosonCoherentKet(alpha2)).doit() -
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exp((alpha1 - alpha2) ** 2 * Rational(-1, 2))) < 1e-12
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assert qapply(a * BosonCoherentKet(alpha1)) == \
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alpha1 * BosonCoherentKet(alpha1)
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