def test_innerproduct():
j, m = symbols("j m")
assert InnerProduct(JzBra(1, 1), JzKet(1, 1)).doit() == 1
assert InnerProduct(JzBra(S(1) / 2,
S(1) / 2), JzKet(S(1) / 2,
-S(1) / 2)).doit() == 0
assert InnerProduct(JzBra(j, m), JzKet(j, m)).doit() == 1
assert InnerProduct(JzBra(1, 0), JyKet(1, 1)).doit() == I / sqrt(2)
assert InnerProduct(JxBra(S(1) / 2,
S(1) / 2),
JzKet(S(1) / 2,
S(1) / 2)).doit() == -sqrt(2) / 2
assert InnerProduct(JyBra(1, 1), JzKet(1, 1)).doit() == S(1) / 2
assert InnerProduct(JxBra(1, -1), JyKet(1, 1)).doit() == 0
def test_spin():
assert operators_to_state(set([J2Op, JxOp])) == JxKet
assert operators_to_state(set([J2Op, JyOp])) == JyKet
assert operators_to_state(set([J2Op, JzOp])) == JzKet
#FIXME ajgpitch 22 Sept 2019:
# JxKet() etc seems to require positional arguments: 'j' and 'm'
# So these tests cannot work
# Probably easy to work out what 'j' and 'm' should be from the physics
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(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])
#FIXME ajgpitch 22 Sept 2019:
# JxKet() etc seems to require positional arguments: 'j' and 'm'
# So these tests cannot work
# Probably easy to work out what 'j' and 'm' should be from the physics
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()])
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_outer_product():
k = Ket('k')
b = Bra('b')
op = OuterProduct(k, b)
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative is False
op = k*b
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative is False
op = 2*k*b
assert op == Mul(Integer(2), k, b)
op = 2*(k*b)
assert op == Mul(Integer(2), OuterProduct(k, b))
assert Dagger(k*b) == OuterProduct(Dagger(b), Dagger(k))
assert Dagger(k*b).is_commutative is False
#test the _eval_trace
assert Tr(OuterProduct(JzKet(1, 1), JzBra(1, 1))).doit() == 1
# test scaled kets and bras
assert OuterProduct(2 * k, b) == 2 * OuterProduct(k, b)
assert OuterProduct(k, 2 * b) == 2 * OuterProduct(k, b)
# test sums of kets and bras
k1, k2 = Ket('k1'), Ket('k2')
b1, b2 = Bra('b1'), Bra('b2')
assert (OuterProduct(k1 + k2, b1) ==
OuterProduct(k1, b1) + OuterProduct(k2, b1))
assert (OuterProduct(k1, b1 + b2) ==
OuterProduct(k1, b1) + OuterProduct(k1, b2))
assert (OuterProduct(1 * k1 + 2 * k2, 3 * b1 + 4 * b2) ==
3 * OuterProduct(k1, b1) +
4 * OuterProduct(k1, b2) +
6 * OuterProduct(k2, b1) +
8 * OuterProduct(k2, b2))
def test_spin():
assert operators_to_state({J2Op, JxOp}) == JxKet
assert operators_to_state({J2Op, JyOp}) == JyKet
assert operators_to_state({J2Op, JzOp}) == JzKet
assert operators_to_state({J2Op(), JxOp()}) == JxKet
assert operators_to_state({J2Op(), JyOp()}) == JyKet
assert operators_to_state({J2Op(), JzOp()}) == JzKet
assert state_to_operators(JxKet) == {J2Op, JxOp}
assert state_to_operators(JyKet) == {J2Op, JyOp}
assert state_to_operators(JzKet) == {J2Op, JzOp}
assert state_to_operators(JxBra) == {J2Op, JxOp}
assert state_to_operators(JyBra) == {J2Op, JyOp}
assert state_to_operators(JzBra) == {J2Op, JzOp}
assert state_to_operators(JxKet(S.Half, S.Half)) == {J2Op(), JxOp()}
assert state_to_operators(JyKet(S.Half, S.Half)) == {J2Op(), JyOp()}
assert state_to_operators(JzKet(S.Half, S.Half)) == {J2Op(), JzOp()}
assert state_to_operators(JxBra(S.Half, S.Half)) == {J2Op(), JxOp()}
assert state_to_operators(JyBra(S.Half, S.Half)) == {J2Op(), JyOp()}
assert state_to_operators(JzBra(S.Half, S.Half)) == {J2Op(), JzOp()}
def test_spin():
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(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()])
def test_outer_product():
k = Ket('k')
b = Bra('b')
op = OuterProduct(k, b)
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative is False
op = k * b
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative is False
op = 2 * k * b
assert op == Mul(Integer(2), k, b)
op = 2 * (k * b)
assert op == Mul(Integer(2), OuterProduct(k, b))
assert Dagger(k * b) == OuterProduct(Dagger(b), Dagger(k))
assert Dagger(k * b).is_commutative is False
#test the _eval_trace
assert Tr(OuterProduct(JzKet(1, 1), JzBra(1, 1))).doit() == 1
def test_rewrite():
# Rewrite to same basis
assert JxBra(1, 1).rewrite('Jx') == JxBra(1, 1)
assert JxKet(1, 1).rewrite('Jx') == JxKet(1, 1)
# Rewriting to different basis
assert JxKet(1, 1).rewrite('Jy') == I * JyKet(1, 1)
assert JxKet(1, 0).rewrite('Jy') == JyKet(1, 0)
assert JxKet(1, -1).rewrite('Jy') == -I * JyKet(1, -1)
assert JxKet(1, 1).rewrite(
'Jz') == JzKet(1, 1) / 2 + JzKet(1, 0) / sqrt(2) + JzKet(1, -1) / 2
assert JxKet(1, 0).rewrite(
'Jz') == -sqrt(2) * JzKet(1, 1) / 2 + sqrt(2) * JzKet(1, -1) / 2
assert JxKet(1, -1).rewrite(
'Jz') == JzKet(1, 1) / 2 - JzKet(1, 0) / sqrt(2) + JzKet(1, -1) / 2
assert JyKet(1, 1).rewrite('Jx') == -I * JxKet(1, 1)
assert JyKet(1, 0).rewrite('Jx') == JxKet(1, 0)
assert JyKet(1, -1).rewrite('Jx') == I * JxKet(1, -1)
assert JyKet(1, 1).rewrite('Jz') == JzKet(1, 1) / 2 + sqrt(2) * I * JzKet(
1, 0) / 2 - JzKet(1, -1) / 2
assert JyKet(1, 0).rewrite(
'Jz') == sqrt(2) * I * JzKet(1, 1) / 2 + sqrt(2) * I * JzKet(1, -1) / 2
assert JyKet(1,
-1).rewrite('Jz') == -JzKet(1, 1) / 2 + sqrt(2) * I * JzKet(
1, 0) / 2 + JzKet(1, -1) / 2
assert JzKet(1, 1).rewrite(
'Jx') == JxKet(1, 1) / 2 - sqrt(2) * JxKet(1, 0) / 2 + JxKet(1, -1) / 2
assert JzKet(1, 0).rewrite(
'Jx') == sqrt(2) * JxKet(1, 1) / 2 - sqrt(2) * JxKet(1, -1) / 2
assert JzKet(1, -1).rewrite(
'Jx') == JxKet(1, 1) / 2 + sqrt(2) * JxKet(1, 0) / 2 + JxKet(1, -1) / 2
assert JzKet(1, 1).rewrite('Jy') == JyKet(1, 1) / 2 - sqrt(2) * I * JyKet(
1, 0) / 2 - JyKet(1, -1) / 2
assert JzKet(1, 0).rewrite('Jy') == -sqrt(2) * I * JyKet(
1, 1) / 2 - sqrt(2) * I * JyKet(1, -1) / 2
assert JzKet(1,
-1).rewrite('Jy') == -JyKet(1, 1) / 2 - sqrt(2) * I * JyKet(
1, 0) / 2 + JyKet(1, -1) / 2
# Innerproducts of rewritten states
assert qapply(JxBra(1, 1) * JxKet(1, 1).rewrite('Jy')).doit() == 1
assert qapply(JxBra(1, 0) * JxKet(1, 0).rewrite('Jy')).doit() == 1
assert qapply(JxBra(1, -1) * JxKet(1, -1).rewrite('Jy')).doit() == 1
assert qapply(JxBra(1, 1) * JxKet(1, 1).rewrite('Jz')).doit() == 1
assert qapply(JxBra(1, 0) * JxKet(1, 0).rewrite('Jz')).doit() == 1
assert qapply(JxBra(1, -1) * JxKet(1, -1).rewrite('Jz')).doit() == 1
assert qapply(JyBra(1, 1) * JyKet(1, 1).rewrite('Jx')).doit() == 1
assert qapply(JyBra(1, 0) * JyKet(1, 0).rewrite('Jx')).doit() == 1
assert qapply(JyBra(1, -1) * JyKet(1, -1).rewrite('Jx')).doit() == 1
assert qapply(JyBra(1, 1) * JyKet(1, 1).rewrite('Jz')).doit() == 1
assert qapply(JyBra(1, 0) * JyKet(1, 0).rewrite('Jz')).doit() == 1
assert qapply(JyBra(1, -1) * JyKet(1, -1).rewrite('Jz')).doit() == 1
assert qapply(JyBra(1, 1) * JyKet(1, 1).rewrite('Jz')).doit() == 1
assert qapply(JyBra(1, 0) * JyKet(1, 0).rewrite('Jz')).doit() == 1
assert qapply(JyBra(1, -1) * JyKet(1, -1).rewrite('Jz')).doit() == 1
assert qapply(JzBra(1, 1) * JzKet(1, 1).rewrite('Jy')).doit() == 1
assert qapply(JzBra(1, 0) * JzKet(1, 0).rewrite('Jy')).doit() == 1
assert qapply(JzBra(1, -1) * JzKet(1, -1).rewrite('Jy')).doit() == 1
assert qapply(JxBra(1, 1) * JxKet(1, 0).rewrite('Jy')).doit() == 0
assert qapply(JxBra(1, 1) * JxKet(1, -1).rewrite('Jy')) == 0
assert qapply(JxBra(1, 1) * JxKet(1, 0).rewrite('Jz')).doit() == 0
assert qapply(JxBra(1, 1) * JxKet(1, -1).rewrite('Jz')) == 0
assert qapply(JyBra(1, 1) * JyKet(1, 0).rewrite('Jx')).doit() == 0
assert qapply(JyBra(1, 1) * JyKet(1, -1).rewrite('Jx')) == 0
assert qapply(JyBra(1, 1) * JyKet(1, 0).rewrite('Jz')).doit() == 0
assert qapply(JyBra(1, 1) * JyKet(1, -1).rewrite('Jz')) == 0
assert qapply(JzBra(1, 1) * JzKet(1, 0).rewrite('Jx')).doit() == 0
assert qapply(JzBra(1, 1) * JzKet(1, -1).rewrite('Jx')) == 0
assert qapply(JzBra(1, 1) * JzKet(1, 0).rewrite('Jy')).doit() == 0
assert qapply(JzBra(1, 1) * JzKet(1, -1).rewrite('Jy')) == 0
assert qapply(JxBra(1, 0) * JxKet(1, 1).rewrite('Jy')) == 0
assert qapply(JxBra(1, 0) * JxKet(1, -1).rewrite('Jy')) == 0
assert qapply(JxBra(1, 0) * JxKet(1, 1).rewrite('Jz')) == 0
assert qapply(JxBra(1, 0) * JxKet(1, -1).rewrite('Jz')) == 0
assert qapply(JyBra(1, 0) * JyKet(1, 1).rewrite('Jx')) == 0
assert qapply(JyBra(1, 0) * JyKet(1, -1).rewrite('Jx')) == 0
assert qapply(JyBra(1, 0) * JyKet(1, 1).rewrite('Jz')) == 0
assert qapply(JyBra(1, 0) * JyKet(1, -1).rewrite('Jz')) == 0
assert qapply(JzBra(1, 0) * JzKet(1, 1).rewrite('Jx')) == 0
assert qapply(JzBra(1, 0) * JzKet(1, -1).rewrite('Jx')) == 0
assert qapply(JzBra(1, 0) * JzKet(1, 1).rewrite('Jy')) == 0
assert qapply(JzBra(1, 0) * JzKet(1, -1).rewrite('Jy')) == 0
assert qapply(JxBra(1, -1) * JxKet(1, 1).rewrite('Jy')) == 0
assert qapply(JxBra(1, -1) * JxKet(1, 0).rewrite('Jy')).doit() == 0
assert qapply(JxBra(1, -1) * JxKet(1, 1).rewrite('Jz')) == 0
assert qapply(JxBra(1, -1) * JxKet(1, 0).rewrite('Jz')).doit() == 0
assert qapply(JyBra(1, -1) * JyKet(1, 1).rewrite('Jx')) == 0
assert qapply(JyBra(1, -1) * JyKet(1, 0).rewrite('Jx')).doit() == 0
assert qapply(JyBra(1, -1) * JyKet(1, 1).rewrite('Jz')) == 0
assert qapply(JyBra(1, -1) * JyKet(1, 0).rewrite('Jz')).doit() == 0
assert qapply(JzBra(1, -1) * JzKet(1, 1).rewrite('Jx')) == 0
assert qapply(JzBra(1, -1) * JzKet(1, 0).rewrite('Jx')).doit() == 0
assert qapply(JzBra(1, -1) * JzKet(1, 1).rewrite('Jy')) == 0
assert qapply(JzBra(1, -1) * JzKet(1, 0).rewrite('Jy')).doit() == 0
def test_sympy__physics__quantum__spin__JzBra():
from sympy.physics.quantum.spin import JzBra
assert _test_args(JzBra(1, 0))
def test_big_expr():
f = Function('f')
x = symbols('x')
e1 = Dagger(
AntiCommutator(
Operator('A') + Operator('B'),
Pow(DifferentialOperator(Derivative(f(x), x), f(x)), 3)) *
TensorProduct(Jz**2,
Operator('A') + Operator('B'))) * (JzBra(1, 0) + JzBra(
1, 1)) * (JzKet(0, 0) + JzKet(1, -1))
e2 = Commutator(Jz**2,
Operator('A') + Operator('B')) * AntiCommutator(
Dagger(Operator('C') * Operator('D')),
Operator('E').inv()**2) * Dagger(Commutator(Jz, J2))
e3 = Wigner3j(1, 2, 3, 4, 5, 6) * TensorProduct(
Commutator(
Operator('A') + Dagger(Operator('B')),
Operator('C') + Operator('D')), Jz - J2) * Dagger(
OuterProduct(Dagger(JzBra(1, 1)), JzBra(
1, 0))) * TensorProduct(
JzKetCoupled(1, 1,
(1, 1)) + JzKetCoupled(1, 0, (1, 1)),
JzKetCoupled(1, -1, (1, 1)))
e4 = (ComplexSpace(1) * ComplexSpace(2) +
FockSpace()**2) * (L2(Interval(0, oo)) + HilbertSpace())
assert str(
e1
) == '(Jz**2)x(Dagger(A) + Dagger(B))*{Dagger(DifferentialOperator(Derivative(f(x), x),f(x)))**3,Dagger(A) + Dagger(B)}*(<1,0| + <1,1|)*(|0,0> + |1,-1>)'
ascii_str = \
"""\
/ 3 \\ \n\
|/ +\\ | \n\
2 / + +\\ <| /d \\ | + +> \n\
/J \\ x \\A + B /*||DifferentialOperator|--(f(x)),f(x)| | ,A + B |*(<1,0| + <1,1|)*(|0,0> + |1,-1>)\n\
\\ z/ \\\\ \dx / / / \
"""
ucode_str = \
u"""\
⎧ 3 ⎫ \n\
⎪⎛ †⎞ ⎪ \n\
2 ⎛ † †⎞ ⎨⎜ ⎛d ⎞ ⎟ † †⎬ \n\
⎛J ⎞ ⨂ ⎝A + B ⎠⋅⎪⎜DifferentialOperator⎜──(f(x)),f(x)⎟ ⎟ ,A + B ⎪⋅(⟨1,0❘ + ⟨1,1❘)⋅(❘0,0⟩ + ❘1,-1⟩)\n\
⎝ z⎠ ⎩⎝ ⎝dx ⎠ ⎠ ⎭ \
"""
assert pretty(e1) == ascii_str
assert upretty(e1) == ucode_str
assert latex(e1) == \
r'{\left(J_z\right)^{2}}\otimes \left({A^{\dag} + B^{\dag}}\right) \left\{\left(DifferentialOperator\left(\frac{\partial}{\partial x} \operatorname{f}{\left (x \right )},\operatorname{f}{\left (x \right )}\right)^{\dag}\right)^{3},A^{\dag} + B^{\dag}\right\} \left({\left\langle 1,0\right|} + {\left\langle 1,1\right|}\right) \left({\left|0,0\right\rangle } + {\left|1,-1\right\rangle }\right)'
sT(
e1,
"Mul(TensorProduct(Pow(JzOp(Symbol('J')), Integer(2)), Add(Dagger(Operator(Symbol('A'))), Dagger(Operator(Symbol('B'))))), AntiCommutator(Pow(Dagger(DifferentialOperator(Derivative(Function('f')(Symbol('x')), Symbol('x')),Function('f')(Symbol('x')))), Integer(3)),Add(Dagger(Operator(Symbol('A'))), Dagger(Operator(Symbol('B'))))), Add(JzBra(Integer(1),Integer(0)), JzBra(Integer(1),Integer(1))), Add(JzKet(Integer(0),Integer(0)), JzKet(Integer(1),Integer(-1))))"
)
assert str(e2) == '[Jz**2,A + B]*{E**(-2),Dagger(D)*Dagger(C)}*[J2,Jz]'
ascii_str = \
"""\
[ 2 ] / -2 + +\\ [ 2 ]\n\
[/J \\ ,A + B]*<E ,D *C >*[J ,J ]\n\
[\\ z/ ] \\ / [ z]\
"""
ucode_str = \
u"""\
⎡ 2 ⎤ ⎧ -2 † †⎫ ⎡ 2 ⎤\n\
⎢⎛J ⎞ ,A + B⎥⋅⎨E ,D ⋅C ⎬⋅⎢J ,J ⎥\n\
⎣⎝ z⎠ ⎦ ⎩ ⎭ ⎣ z⎦\
"""
assert pretty(e2) == ascii_str
assert upretty(e2) == ucode_str
assert latex(e2) == \
r'\left[\left(J_z\right)^{2},A + B\right] \left\{\left(E\right)^{-2},D^{\dag} C^{\dag}\right\} \left[J^2,J_z\right]'
sT(
e2,
"Mul(Commutator(Pow(JzOp(Symbol('J')), Integer(2)),Add(Operator(Symbol('A')), Operator(Symbol('B')))), AntiCommutator(Pow(Operator(Symbol('E')), Integer(-2)),Mul(Dagger(Operator(Symbol('D'))), Dagger(Operator(Symbol('C'))))), Commutator(J2Op(Symbol('J')),JzOp(Symbol('J'))))"
)
assert str(e3) == \
"Wigner3j(1, 2, 3, 4, 5, 6)*[Dagger(B) + A,C + D]x(-J2 + Jz)*|1,0><1,1|*(|1,0,j1=1,j2=1> + |1,1,j1=1,j2=1>)x|1,-1,j1=1,j2=1>"
ascii_str = \
"""\
[ + ] / 2 \\ \n\
/1 3 5\\*[B + A,C + D]x |- J + J |*|1,0><1,1|*(|1,0,j1=1,j2=1> + |1,1,j1=1,j2=1>)x |1,-1,j1=1,j2=1>\n\
| | \\ z/ \n\
\\2 4 6/ \
"""
ucode_str = \
u"""\
⎡ † ⎤ ⎛ 2 ⎞ \n\
⎛1 3 5⎞⋅⎣B + A,C + D⎦⨂ ⎜- J + J ⎟⋅❘1,0⟩⟨1,1❘⋅(❘1,0,j₁=1,j₂=1⟩ + ❘1,1,j₁=1,j₂=1⟩)⨂ ❘1,-1,j₁=1,j₂=1⟩\n\
⎜ ⎟ ⎝ z⎠ \n\
⎝2 4 6⎠ \
"""
assert pretty(e3) == ascii_str
assert upretty(e3) == ucode_str
assert latex(e3) == \
r'\left(\begin{array}{ccc} 1 & 3 & 5 \\ 2 & 4 & 6 \end{array}\right) {\left[B^{\dag} + A,C + D\right]}\otimes \left({- J^2 + J_z}\right) {\left|1,0\right\rangle }{\left\langle 1,1\right|} \left({{\left|1,0,j_{1}=1,j_{2}=1\right\rangle } + {\left|1,1,j_{1}=1,j_{2}=1\right\rangle }}\right)\otimes {{\left|1,-1,j_{1}=1,j_{2}=1\right\rangle }}'
sT(
e3,
"Mul(Wigner3j(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6)), TensorProduct(Commutator(Add(Dagger(Operator(Symbol('B'))), Operator(Symbol('A'))),Add(Operator(Symbol('C')), Operator(Symbol('D')))), Add(Mul(Integer(-1), J2Op(Symbol('J'))), JzOp(Symbol('J')))), OuterProduct(JzKet(Integer(1),Integer(0)),JzBra(Integer(1),Integer(1))), TensorProduct(Add(JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1)))), JzKetCoupled(Integer(1),Integer(1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))), JzKetCoupled(Integer(1),Integer(-1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))))"
)
assert str(e4) == '(C(1)*C(2)+F**2)*(L2([0, oo))+H)'
ascii_str = \
"""\
// 1 2\\ x2\\ / 2 \\\n\
\\\\C x C / + F / x \L + H/\
"""
ucode_str = \
u"""\
⎛⎛ 1 2⎞ ⨂2⎞ ⎛ 2 ⎞\n\
⎝⎝C ⨂ C ⎠ ⊕ F ⎠ ⨂ ⎝L ⊕ H⎠\
"""
assert pretty(e4) == ascii_str
assert upretty(e4) == ucode_str
assert latex(e4) == \
r'\left(\left(\mathcal{C}^{1}\otimes \mathcal{C}^{2}\right)\oplus {\mathcal{F}}^{\otimes 2}\right)\otimes \left({\mathcal{L}^2}\left( \left[0, \infty\right) \right)\oplus \mathcal{H}\right)'
sT(
e4,
"TensorProductHilbertSpace((DirectSumHilbertSpace(TensorProductHilbertSpace(ComplexSpace(Integer(1)),ComplexSpace(Integer(2))),TensorPowerHilbertSpace(FockSpace(),Integer(2)))),(DirectSumHilbertSpace(L2(Interval(Integer(0), oo, False, True)),HilbertSpace())))"
)
def test_spin():
lz = JzOp('L')
ket = JzKet(1, 0)
bra = JzBra(1, 0)
cket = JzKetCoupled(1, 0, (1, 2))
cbra = JzBraCoupled(1, 0, (1, 2))
cket_big = JzKetCoupled(1, 0, (1, 2, 3))
cbra_big = JzBraCoupled(1, 0, (1, 2, 3))
rot = Rotation(1, 2, 3)
bigd = WignerD(1, 2, 3, 4, 5, 6)
smalld = WignerD(1, 2, 3, 0, 4, 0)
assert str(lz) == 'Lz'
ascii_str = \
"""\
L \n\
z\
"""
ucode_str = \
u"""\
L \n\
z\
"""
assert pretty(lz) == ascii_str
assert upretty(lz) == ucode_str
assert latex(lz) == 'L_z'
sT(lz, "JzOp(Symbol('L'))")
assert str(J2) == 'J2'
ascii_str = \
"""\
2\n\
J \
"""
ucode_str = \
u"""\
2\n\
J \
"""
assert pretty(J2) == ascii_str
assert upretty(J2) == ucode_str
assert latex(J2) == r'J^2'
sT(J2, "J2Op(Symbol('J'))")
assert str(Jz) == 'Jz'
ascii_str = \
"""\
J \n\
z\
"""
ucode_str = \
u"""\
J \n\
z\
"""
assert pretty(Jz) == ascii_str
assert upretty(Jz) == ucode_str
assert latex(Jz) == 'J_z'
sT(Jz, "JzOp(Symbol('J'))")
assert str(ket) == '|1,0>'
assert pretty(ket) == '|1,0>'
assert upretty(ket) == u'❘1,0⟩'
assert latex(ket) == r'{\left|1,0\right\rangle }'
sT(ket, "JzKet(Integer(1),Integer(0))")
assert str(bra) == '<1,0|'
assert pretty(bra) == '<1,0|'
assert upretty(bra) == u'⟨1,0❘'
assert latex(bra) == r'{\left\langle 1,0\right|}'
sT(bra, "JzBra(Integer(1),Integer(0))")
assert str(cket) == '|1,0,j1=1,j2=2>'
assert pretty(cket) == '|1,0,j1=1,j2=2>'
assert upretty(cket) == u'❘1,0,j₁=1,j₂=2⟩'
assert latex(cket) == r'{\left|1,0,j_{1}=1,j_{2}=2\right\rangle }'
sT(
cket,
"JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))"
)
assert str(cbra) == '<1,0,j1=1,j2=2|'
assert pretty(cbra) == '<1,0,j1=1,j2=2|'
assert upretty(cbra) == u'⟨1,0,j₁=1,j₂=2❘'
assert latex(cbra) == r'{\left\langle 1,0,j_{1}=1,j_{2}=2\right|}'
sT(
cbra,
"JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))"
)
assert str(cket_big) == '|1,0,j1=1,j2=2,j3=3,j(1,2)=3>'
# TODO: Fix non-unicode pretty printing
# i.e. j1,2 -> j(1,2)
assert pretty(cket_big) == '|1,0,j1=1,j2=2,j3=3,j1,2=3>'
assert upretty(cket_big) == u'❘1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3⟩'
assert latex(cket_big) == \
r'{\left|1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right\rangle }'
sT(
cket_big,
"JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))"
)
assert str(cbra_big) == '<1,0,j1=1,j2=2,j3=3,j(1,2)=3|'
assert pretty(cbra_big) == u'<1,0,j1=1,j2=2,j3=3,j1,2=3|'
assert upretty(cbra_big) == u'⟨1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3❘'
assert latex(cbra_big) == \
r'{\left\langle 1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right|}'
sT(
cbra_big,
"JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))"
)
assert str(rot) == 'R(1,2,3)'
assert pretty(rot) == 'R (1,2,3)'
assert upretty(rot) == u'ℛ (1,2,3)'
assert latex(rot) == r'\mathcal{R}\left(1,2,3\right)'
sT(rot, "Rotation(Integer(1),Integer(2),Integer(3))")
assert str(bigd) == 'WignerD(1, 2, 3, 4, 5, 6)'
ascii_str = \
"""\
1 \n\
D (4,5,6)\n\
2,3 \
"""
ucode_str = \
u"""\
1 \n\
D (4,5,6)\n\
2,3 \
"""
assert pretty(bigd) == ascii_str
assert upretty(bigd) == ucode_str
assert latex(bigd) == r'D^{1}_{2,3}\left(4,5,6\right)'
sT(
bigd,
"WignerD(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))"
)
assert str(smalld) == 'WignerD(1, 2, 3, 0, 4, 0)'
ascii_str = \
"""\
1 \n\
d (4)\n\
2,3 \
"""
ucode_str = \
u"""\
1 \n\
d (4)\n\
2,3 \
"""
assert pretty(smalld) == ascii_str
assert upretty(smalld) == ucode_str
assert latex(smalld) == r'd^{1}_{2,3}\left(4\right)'
sT(
smalld,
"WignerD(Integer(1), Integer(2), Integer(3), Integer(0), Integer(4), Integer(0))"
)
def test_innerproduct():
x = symbols('x')
ip1 = InnerProduct(Bra(), Ket())
ip2 = InnerProduct(TimeDepBra(), TimeDepKet())
ip3 = InnerProduct(JzBra(1, 1), JzKet(1, 1))
ip4 = InnerProduct(JzBraCoupled(1, 1, (1, 1)), JzKetCoupled(1, 1, (1, 1)))
ip_tall1 = InnerProduct(Bra(x / 2), Ket(x / 2))
ip_tall2 = InnerProduct(Bra(x), Ket(x / 2))
ip_tall3 = InnerProduct(Bra(x / 2), Ket(x))
assert str(ip1) == '<psi|psi>'
assert pretty(ip1) == '<psi|psi>'
assert upretty(ip1) == u'⟨ψ❘ψ⟩'
assert latex(
ip1) == r'\left\langle \psi \right. {\left|\psi\right\rangle }'
sT(ip1, "InnerProduct(Bra(Symbol('psi')),Ket(Symbol('psi')))")
assert str(ip2) == '<psi;t|psi;t>'
assert pretty(ip2) == '<psi;t|psi;t>'
assert upretty(ip2) == u'⟨ψ;t❘ψ;t⟩'
assert latex(ip2) == \
r'\left\langle \psi;t \right. {\left|\psi;t\right\rangle }'
sT(
ip2,
"InnerProduct(TimeDepBra(Symbol('psi'),Symbol('t')),TimeDepKet(Symbol('psi'),Symbol('t')))"
)
assert str(ip3) == "<1,1|1,1>"
assert pretty(ip3) == '<1,1|1,1>'
assert upretty(ip3) == u'⟨1,1❘1,1⟩'
assert latex(ip3) == r'\left\langle 1,1 \right. {\left|1,1\right\rangle }'
sT(
ip3,
"InnerProduct(JzBra(Integer(1),Integer(1)),JzKet(Integer(1),Integer(1)))"
)
assert str(ip4) == "<1,1,j1=1,j2=1|1,1,j1=1,j2=1>"
assert pretty(ip4) == '<1,1,j1=1,j2=1|1,1,j1=1,j2=1>'
assert upretty(ip4) == u'⟨1,1,j₁=1,j₂=1❘1,1,j₁=1,j₂=1⟩'
assert latex(ip4) == \
r'\left\langle 1,1,j_{1}=1,j_{2}=1 \right. {\left|1,1,j_{1}=1,j_{2}=1\right\rangle }'
sT(
ip4,
"InnerProduct(JzBraCoupled(Integer(1),Integer(1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1)))),JzKetCoupled(Integer(1),Integer(1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1)))))"
)
assert str(ip_tall1) == '<x/2|x/2>'
ascii_str = \
"""\
/ | \\ \n\
/ x|x \\\n\
\\ -|- /\n\
\\2|2/ \
"""
ucode_str = \
u"""\
╱ │ ╲ \n\
╱ x│x ╲\n\
╲ ─│─ ╱\n\
╲2│2╱ \
"""
assert pretty(ip_tall1) == ascii_str
assert upretty(ip_tall1) == ucode_str
assert latex(ip_tall1) == \
r'\left\langle \frac{1}{2} x \right. {\left|\frac{1}{2} x\right\rangle }'
sT(
ip_tall1,
"InnerProduct(Bra(Mul(Rational(1, 2), Symbol('x'))),Ket(Mul(Rational(1, 2), Symbol('x'))))"
)
assert str(ip_tall2) == '<x|x/2>'
ascii_str = \
"""\
/ | \\ \n\
/ |x \\\n\
\\ x|- /\n\
\\ |2/ \
"""
ucode_str = \
u"""\
╱ │ ╲ \n\
╱ │x ╲\n\
╲ x│─ ╱\n\
╲ │2╱ \
"""
assert pretty(ip_tall2) == ascii_str
assert upretty(ip_tall2) == ucode_str
assert latex(ip_tall2) == \
r'\left\langle x \right. {\left|\frac{1}{2} x\right\rangle }'
sT(ip_tall2,
"InnerProduct(Bra(Symbol('x')),Ket(Mul(Rational(1, 2), Symbol('x'))))")
assert str(ip_tall3) == '<x/2|x>'
ascii_str = \
"""\
/ | \\ \n\
/ x| \\\n\
\\ -|x /\n\
\\2| / \
"""
ucode_str = \
u"""\
╱ │ ╲ \n\
╱ x│ ╲\n\
╲ ─│x ╱\n\
╲2│ ╱ \
"""
assert pretty(ip_tall3) == ascii_str
assert upretty(ip_tall3) == ucode_str
assert latex(ip_tall3) == \
r'\left\langle \frac{1}{2} x \right. {\left|x\right\rangle }'
sT(ip_tall3,
"InnerProduct(Bra(Mul(Rational(1, 2), Symbol('x'))),Ket(Symbol('x')))")
def test_spin():
lz = JzOp("L")
ket = JzKet(1, 0)
bra = JzBra(1, 0)
cket = JzKetCoupled(1, 0, (1, 2))
cbra = JzBraCoupled(1, 0, (1, 2))
cket_big = JzKetCoupled(1, 0, (1, 2, 3))
cbra_big = JzBraCoupled(1, 0, (1, 2, 3))
rot = Rotation(1, 2, 3)
bigd = WignerD(1, 2, 3, 4, 5, 6)
smalld = WignerD(1, 2, 3, 0, 4, 0)
assert str(lz) == "Lz"
ascii_str = """\
L \n\
z\
"""
ucode_str = u("""\
L \n\
z\
""")
assert pretty(lz) == ascii_str
assert upretty(lz) == ucode_str
assert latex(lz) == "L_z"
sT(lz, "JzOp(Symbol('L'))")
assert str(J2) == "J2"
ascii_str = """\
2\n\
J \
"""
ucode_str = u("""\
2\n\
J \
""")
assert pretty(J2) == ascii_str
assert upretty(J2) == ucode_str
assert latex(J2) == r"J^2"
sT(J2, "J2Op(Symbol('J'))")
assert str(Jz) == "Jz"
ascii_str = """\
J \n\
z\
"""
ucode_str = u("""\
J \n\
z\
""")
assert pretty(Jz) == ascii_str
assert upretty(Jz) == ucode_str
assert latex(Jz) == "J_z"
sT(Jz, "JzOp(Symbol('J'))")
assert str(ket) == "|1,0>"
assert pretty(ket) == "|1,0>"
assert upretty(ket) == u"❘1,0⟩"
assert latex(ket) == r"{\left|1,0\right\rangle }"
sT(ket, "JzKet(Integer(1),Integer(0))")
assert str(bra) == "<1,0|"
assert pretty(bra) == "<1,0|"
assert upretty(bra) == u"⟨1,0❘"
assert latex(bra) == r"{\left\langle 1,0\right|}"
sT(bra, "JzBra(Integer(1),Integer(0))")
assert str(cket) == "|1,0,j1=1,j2=2>"
assert pretty(cket) == "|1,0,j1=1,j2=2>"
assert upretty(cket) == u"❘1,0,j₁=1,j₂=2⟩"
assert latex(cket) == r"{\left|1,0,j_{1}=1,j_{2}=2\right\rangle }"
sT(
cket,
"JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))",
)
assert str(cbra) == "<1,0,j1=1,j2=2|"
assert pretty(cbra) == "<1,0,j1=1,j2=2|"
assert upretty(cbra) == u"⟨1,0,j₁=1,j₂=2❘"
assert latex(cbra) == r"{\left\langle 1,0,j_{1}=1,j_{2}=2\right|}"
sT(
cbra,
"JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))",
)
assert str(cket_big) == "|1,0,j1=1,j2=2,j3=3,j(1,2)=3>"
# TODO: Fix non-unicode pretty printing
# i.e. j1,2 -> j(1,2)
assert pretty(cket_big) == "|1,0,j1=1,j2=2,j3=3,j1,2=3>"
assert upretty(cket_big) == u"❘1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3⟩"
assert (latex(cket_big) ==
r"{\left|1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right\rangle }")
sT(
cket_big,
"JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))",
)
assert str(cbra_big) == "<1,0,j1=1,j2=2,j3=3,j(1,2)=3|"
assert pretty(cbra_big) == u"<1,0,j1=1,j2=2,j3=3,j1,2=3|"
assert upretty(cbra_big) == u"⟨1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3❘"
assert (latex(cbra_big) ==
r"{\left\langle 1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right|}")
sT(
cbra_big,
"JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))",
)
assert str(rot) == "R(1,2,3)"
assert pretty(rot) == "R (1,2,3)"
assert upretty(rot) == u"ℛ (1,2,3)"
assert latex(rot) == r"\mathcal{R}\left(1,2,3\right)"
sT(rot, "Rotation(Integer(1),Integer(2),Integer(3))")
assert str(bigd) == "WignerD(1, 2, 3, 4, 5, 6)"
ascii_str = """\
1 \n\
D (4,5,6)\n\
2,3 \
"""
ucode_str = u("""\
1 \n\
D (4,5,6)\n\
2,3 \
""")
assert pretty(bigd) == ascii_str
assert upretty(bigd) == ucode_str
assert latex(bigd) == r"D^{1}_{2,3}\left(4,5,6\right)"
sT(
bigd,
"WignerD(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))",
)
assert str(smalld) == "WignerD(1, 2, 3, 0, 4, 0)"
ascii_str = """\
1 \n\
d (4)\n\
2,3 \
"""
ucode_str = u("""\
1 \n\
d (4)\n\
2,3 \
""")
assert pretty(smalld) == ascii_str
assert upretty(smalld) == ucode_str
assert latex(smalld) == r"d^{1}_{2,3}\left(4\right)"
sT(
smalld,
"WignerD(Integer(1), Integer(2), Integer(3), Integer(0), Integer(4), Integer(0))",
)