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