def test_normal_order():
a = BosonOp('a')
b = BosonOp('b')
c = FermionOp('c')
d = FermionOp('d')
assert normal_order(a * Dagger(a)) == Dagger(a) * a
assert normal_order(Dagger(a) * a) == Dagger(a) * a
assert normal_order(a * Dagger(a)**2) == Dagger(a)**2 * a
assert normal_order(c * Dagger(c)) == -Dagger(c) * c
assert normal_order(Dagger(c) * c) == Dagger(c) * c
assert normal_order(c * Dagger(c)**2) == Dagger(c)**2 * c
def test_tensorproduct():
a = BosonOp("a")
b = BosonOp("b")
ket1 = TensorProduct(BosonFockKet(1), BosonFockKet(2))
ket2 = TensorProduct(BosonFockKet(0), BosonFockKet(0))
ket3 = TensorProduct(BosonFockKet(0), BosonFockKet(2))
bra1 = TensorProduct(BosonFockBra(0), BosonFockBra(0))
bra2 = TensorProduct(BosonFockBra(1), BosonFockBra(2))
assert qapply(TensorProduct(a, b**2) * ket1) == sqrt(2) * ket2
assert qapply(TensorProduct(a, Dagger(b) * b) * ket1) == 2 * ket3
assert qapply(bra1 * TensorProduct(a, b * b),
dagger=True) == sqrt(2) * bra2
assert qapply(bra2 * ket1).doit() == TensorProduct(1, 1)
assert qapply(TensorProduct(a, b * b) * ket1) == sqrt(2) * ket2
assert qapply(Dagger(TensorProduct(a, b * b) * ket1),
dagger=True) == sqrt(2) * Dagger(ket2)
def test_normal_ordered_form():
a = BosonOp('a')
b = BosonOp('b')
c = FermionOp('c')
d = FermionOp('d')
assert normal_ordered_form(Dagger(a) * a) == Dagger(a) * a
assert normal_ordered_form(a * Dagger(a)) == 1 + Dagger(a) * a
assert normal_ordered_form(a ** 2 * Dagger(a)) == \
2 * a + Dagger(a) * a ** 2
assert normal_ordered_form(a ** 3 * Dagger(a)) == \
3 * a ** 2 + Dagger(a) * a ** 3
assert normal_ordered_form(Dagger(c) * c) == Dagger(c) * c
assert normal_ordered_form(c * Dagger(c)) == 1 - Dagger(c) * c
assert normal_ordered_form(c**2 * Dagger(c)) == Dagger(c) * c**2
assert normal_ordered_form(c ** 3 * Dagger(c)) == \
c ** 2 - Dagger(c) * c ** 3
def test_normal_order():
a = BosonOp("a")
c = FermionOp("c")
assert normal_order(a * Dagger(a)) == Dagger(a) * a
assert normal_order(Dagger(a) * a) == Dagger(a) * a
assert normal_order(a * Dagger(a)**2) == Dagger(a)**2 * a
assert normal_order(c * Dagger(c)) == -Dagger(c) * c
assert normal_order(Dagger(c) * c) == Dagger(c) * c
assert normal_order(c * Dagger(c)**2) == Dagger(c)**2 * c
def test_normal_ordered_form():
a = BosonOp("a")
c = FermionOp("c")
assert normal_ordered_form(Dagger(a) * a) == Dagger(a) * a
assert normal_ordered_form(a * Dagger(a)) == 1 + Dagger(a) * a
assert normal_ordered_form(a**2 * Dagger(a)) == 2 * a + Dagger(a) * a**2
assert normal_ordered_form(a**3 * Dagger(a)) == 3 * a**2 + Dagger(a) * a**3
assert normal_ordered_form(Dagger(c) * c) == Dagger(c) * c
assert normal_ordered_form(c * Dagger(c)) == 1 - Dagger(c) * c
assert normal_ordered_form(c**2 * Dagger(c)) == Dagger(c) * c**2
assert normal_ordered_form(c**3 * Dagger(c)) == c**2 - Dagger(c) * c**3
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
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)