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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)
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