def test_enumerate_states():
test = XKet("foo")
assert enumerate_states(test, 1, 1) == [XKet("foo_1")]
assert enumerate_states(
test, [1, 2, 4]) == [XKet("foo_1"),
XKet("foo_2"),
XKet("foo_4")]
def test_innerprod_represent():
assert rep_innerproduct(x_ket) == InnerProduct(XBra("x_1"), x_ket).doit()
assert rep_innerproduct(x_bra) == InnerProduct(x_bra, XKet("x_1")).doit()
try:
rep_innerproduct(x_op)
except TypeError:
return True
def test_op_to_state():
assert operators_to_state(XOp) == XKet()
assert operators_to_state(PxOp) == PxKet()
assert operators_to_state(Operator) == Ket()
assert state_to_operators(operators_to_state(XOp("Q"))) == XOp("Q")
assert state_to_operators(operators_to_state(XOp())) == XOp()
raises(NotImplementedError, lambda: operators_to_state(XKet))
def test_p():
assert Px.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
assert qapply(Px*PxKet(px)) == px*PxKet(px)
assert PxKet(px).dual_class() == PxBra
assert PxBra(x).dual_class() == PxKet
assert (Dagger(PxKet(py))*PxKet(px)).doit() == DiracDelta(px-py)
assert (XBra(x)*PxKet(px)).doit() ==\
exp(I*x*px/hbar)/sqrt(2*pi*hbar)
assert represent(PxKet(px)) == DiracDelta(px-px_1)
rep_x = represent(PxOp(), basis = XOp)
assert rep_x == -hbar*I*DiracDelta(x_1 - x_2)*DifferentialOperator(x_1)
assert rep_x == represent(PxOp(), basis = XOp())
assert rep_x == represent(PxOp(), basis = XKet)
assert rep_x == represent(PxOp(), basis = XKet())
assert represent(PxOp()*XKet(), basis=XKet) == \
-hbar*I*DiracDelta(x - x_2)*DifferentialOperator(x)
assert represent(XBra("y")*PxOp()*XKet(), basis=XKet) == \
-hbar*I*DiracDelta(x-y)*DifferentialOperator(x)
def test_state_to_op():
assert state_to_operators(XKet) == XOp()
assert state_to_operators(PxKet) == PxOp()
assert state_to_operators(XBra) == XOp()
assert state_to_operators(PxBra) == PxOp()
assert state_to_operators(Ket) == Operator()
assert state_to_operators(Bra) == Operator()
assert state_to_operators(JxKet) == set([J2Op(), JxOp()])
assert state_to_operators(JyKet) == set([J2Op(), JyOp()])
assert state_to_operators(JzKet) == set([J2Op(), JzOp()])
assert state_to_operators(JxBra) == set([J2Op(), JxOp()])
assert state_to_operators(JyBra) == set([J2Op(), JyOp()])
assert state_to_operators(JzBra) == set([J2Op(), JzOp()])
assert state_to_operators(JxKet()) == set([J2Op(), JxOp()])
assert state_to_operators(JyKet()) == set([J2Op(), JyOp()])
assert state_to_operators(JzKet()) == set([J2Op(), JzOp()])
assert state_to_operators(JxBra()) == set([J2Op(), JxOp()])
assert state_to_operators(JyBra()) == set([J2Op(), JyOp()])
assert state_to_operators(JzBra()) == set([J2Op(), JzOp()])
assert operators_to_state(state_to_operators(XKet("test"))) == XKet("test")
assert operators_to_state(state_to_operators(XBra("test"))) == XKet("test")
assert operators_to_state(state_to_operators(XKet())) == XKet()
assert operators_to_state(state_to_operators(XBra())) == XKet()
raises(NotImplementedError, 'state_to_operators(XOp)')
def test_x():
assert X.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
assert Commutator(X, Px).doit() == I*hbar
assert apply_operators(X*XKet(x)) == x*XKet(x)
assert XKet(x).dual_class == XBra
assert XBra(x).dual_class == XKet
assert (Dagger(XKet(y))*XKet(x)).doit() == DiracDelta(x-y)
assert (PxBra(px)*XKet(x)).doit() ==\
exp(-I*x*px/hbar)/sqrt(2*pi*hbar)
assert represent(XKet(x)) == x
assert XBra(x).position == x
def test_represent():
x, y = symbols('x y')
d = Density([XKet(), 0.5], [PxKet(), 0.5])
assert (represent(0.5 * (PxKet() * Dagger(PxKet()))) +
represent(0.5 * (XKet() * Dagger(XKet())))) == represent(d)
# check for kets with expr in them
d_with_sym = Density([XKet(x * y), 0.5], [PxKet(x * y), 0.5])
assert (represent(0.5*(PxKet(x*y)*Dagger(PxKet(x*y)))) +
represent(0.5*(XKet(x*y)*Dagger(XKet(x*y))))) == \
represent(d_with_sym)
# check when given explicit basis
assert (represent(0.5*(XKet()*Dagger(XKet())), basis=PxOp()) +
represent(0.5*(PxKet()*Dagger(PxKet())), basis=PxOp())) == \
represent(d, basis=PxOp())
def test_doit():
x, y = symbols('x y')
d = Density([XKet(), 0.5], [PxKet(), 0.5])
assert (0.5 * (PxKet() * Dagger(PxKet())) + 0.5 *
(XKet() * Dagger(XKet()))) == d.doit()
# check for kets with expr in them
d_with_sym = Density([XKet(x * y), 0.5], [PxKet(x * y), 0.5])
assert (0.5 * (PxKet(x * y) * Dagger(PxKet(x * y))) + 0.5 *
(XKet(x * y) * Dagger(XKet(x * y)))) == d_with_sym.doit()
def test_op_to_state():
assert operators_to_state(XOp) == XKet()
assert operators_to_state(PxOp) == PxKet()
assert operators_to_state(Operator) == Ket()
assert operators_to_state(set([J2Op, JxOp])) == JxKet()
assert operators_to_state(set([J2Op, JyOp])) == JyKet()
assert operators_to_state(set([J2Op, JzOp])) == JzKet()
assert operators_to_state(set([J2Op(), JxOp()])) == JxKet()
assert operators_to_state(set([J2Op(), JyOp()])) == JyKet()
assert operators_to_state(set([J2Op(), JzOp()])) == JzKet()
assert state_to_operators(operators_to_state(XOp("Q"))) == XOp("Q")
assert state_to_operators(operators_to_state(XOp())) == XOp()
raises(NotImplementedError, 'operators_to_state(XKet)')
def test_state_to_op():
assert state_to_operators(XKet) == XOp()
assert state_to_operators(PxKet) == PxOp()
assert state_to_operators(XBra) == XOp()
assert state_to_operators(PxBra) == PxOp()
assert state_to_operators(Ket) == Operator()
assert state_to_operators(Bra) == Operator()
assert operators_to_state(state_to_operators(XKet("test"))) == XKet("test")
assert operators_to_state(state_to_operators(XBra("test"))) == XKet("test")
assert operators_to_state(state_to_operators(XKet())) == XKet()
assert operators_to_state(state_to_operators(XBra())) == XKet()
raises(NotImplementedError, lambda: state_to_operators(XOp))
def test_doit():
x, y = symbols('x y')
A, B, C, D, E, F = symbols('A B C D E F', commutative=False)
d = Density([XKet(), 0.5], [PxKet(), 0.5])
assert (0.5 * (PxKet() * Dagger(PxKet())) + 0.5 *
(XKet() * Dagger(XKet()))) == d.doit()
# check for kets with expr in them
d_with_sym = Density([XKet(x * y), 0.5], [PxKet(x * y), 0.5])
assert (0.5 * (PxKet(x * y) * Dagger(PxKet(x * y))) + 0.5 *
(XKet(x * y) * Dagger(XKet(x * y)))) == d_with_sym.doit()
d = Density([(A + B) * C, 1.0])
assert d.doit() == (1.0 * A * C * Dagger(C) * Dagger(A) +
1.0 * A * C * Dagger(C) * Dagger(B) +
1.0 * B * C * Dagger(C) * Dagger(A) +
1.0 * B * C * Dagger(C) * Dagger(B))
# With TensorProducts as args
# Density with simple tensor products as args
t = TensorProduct(A, B, C)
d = Density([t, 1.0])
assert d.doit() == \
1.0 * TensorProduct(A*Dagger(A), B*Dagger(B), C*Dagger(C))
# Density with multiple Tensorproducts as states
t2 = TensorProduct(A, B)
t3 = TensorProduct(C, D)
d = Density([t2, 0.5], [t3, 0.5])
assert d.doit() == (0.5 * TensorProduct(A * Dagger(A), B * Dagger(B)) +
0.5 * TensorProduct(C * Dagger(C), D * Dagger(D)))
#Density with mixed states
d = Density([t2 + t3, 1.0])
assert d.doit() == (1.0 * TensorProduct(A * Dagger(A), B * Dagger(B)) +
1.0 * TensorProduct(A * Dagger(C), B * Dagger(D)) +
1.0 * TensorProduct(C * Dagger(A), D * Dagger(B)) +
1.0 * TensorProduct(C * Dagger(C), D * Dagger(D)))
#Density operators with spin states
tp1 = TensorProduct(JzKet(1, 1), JzKet(1, -1))
d = Density([tp1, 1])
# full trace
t = Tr(d)
assert t.doit() == 1
#Partial trace on density operators with spin states
t = Tr(d, [0])
assert t.doit() == JzKet(1, -1) * Dagger(JzKet(1, -1))
t = Tr(d, [1])
assert t.doit() == JzKet(1, 1) * Dagger(JzKet(1, 1))
# with another spin state
tp2 = TensorProduct(JzKet(S(1) / 2, S(1) / 2), JzKet(S(1) / 2, -S(1) / 2))
d = Density([tp2, 1])
#full trace
t = Tr(d)
assert t.doit() == 1
#Partial trace on density operators with spin states
t = Tr(d, [0])
assert t.doit() == JzKet(S(1) / 2, -S(1) / 2) * Dagger(
JzKet(S(1) / 2, -S(1) / 2))
t = Tr(d, [1])
assert t.doit() == JzKet(S(1) / 2,
S(1) / 2) * Dagger(JzKet(S(1) / 2,
S(1) / 2))
def test_sympy__physics__quantum__cartesian__XKet():
from sympy.physics.quantum.cartesian import XKet
assert _test_args(XKet(x))
def test_x():
assert X.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
assert Commutator(X, Px).doit() == I * hbar
assert qapply(X * XKet(x)) == x * XKet(x)
assert XKet(x).dual_class() == XBra
assert XBra(x).dual_class() == XKet
assert (Dagger(XKet(y)) * XKet(x)).doit() == DiracDelta(x - y)
assert (PxBra(px)*XKet(x)).doit() == \
exp(-I*x*px/hbar)/sqrt(2*pi*hbar)
assert represent(XKet(x)) == DiracDelta(x - x_1)
assert represent(XBra(x)) == DiracDelta(-x + x_1)
assert XBra(x).position == x
assert represent(XOp() * XKet()) == x * DiracDelta(x - x_2)
assert represent(XOp()*XKet()*XBra('y')) == \
x*DiracDelta(x - x_3)*DiracDelta(x_1 - y)
assert represent(XBra("y") * XKet()) == DiracDelta(x - y)
assert represent(XKet() *
XBra()) == DiracDelta(x - x_2) * DiracDelta(x_1 - x)
rep_p = represent(XOp(), basis=PxOp)
assert rep_p == hbar * I * DiracDelta(px_1 -
px_2) * DifferentialOperator(px_1)
assert rep_p == represent(XOp(), basis=PxOp())
assert rep_p == represent(XOp(), basis=PxKet)
assert rep_p == represent(XOp(), basis=PxKet())
assert represent(XOp()*PxKet(), basis=PxKet) == \
hbar*I*DiracDelta(px - px_2)*DifferentialOperator(px)
else:
assert lhs == rhs
def test_scalar_scipy_sparse():
if not np:
skip("numpy not installed.")
if not scipy:
skip("scipy not installed.")
assert represent(Integer(1), format='scipy.sparse') == 1
assert represent(Float(1.0), format='scipy.sparse') == 1.0
assert represent(1.0 + I, format='scipy.sparse') == 1.0 + 1.0j
x_ket = XKet('x')
x_bra = XBra('x')
x_op = XOp('X')
def test_innerprod_represent():
assert rep_innerproduct(x_ket) == InnerProduct(XBra("x_1"), x_ket).doit()
assert rep_innerproduct(x_bra) == InnerProduct(x_bra, XKet("x_1")).doit()
try:
rep_innerproduct(x_op)
except TypeError:
return True
def test_operator_represent():
else:
assert lhs == rhs
def test_scalar_scipy_sparse():
if not np:
skip("numpy not installed.")
if not scipy:
skip("scipy not installed.")
assert represent(Integer(1), format="scipy.sparse") == 1
assert represent(Float(1.0), format="scipy.sparse") == 1.0
assert represent(1.0 + I, format="scipy.sparse") == 1.0 + 1.0j
x_ket = XKet("x")
x_bra = XBra("x")
x_op = XOp("X")
def test_innerprod_represent():
assert rep_innerproduct(x_ket) == InnerProduct(XBra("x_1"), x_ket).doit()
assert rep_innerproduct(x_bra) == InnerProduct(x_bra, XKet("x_1")).doit()
try:
rep_innerproduct(x_op)
except TypeError:
return True
def test_operator_represent():
