def test_time_dep_ket():
k = TimeDepKet(0,t)
assert isinstance(k, TimeDepKet)
assert isinstance(k, KetBase)
assert isinstance(k, StateBase)
assert isinstance(k, QExpr)
assert k.label == (Integer(0),)
assert k.args == (Integer(0),t)
assert k.time == t
assert k.dual_class == TimeDepBra
assert k.dual == TimeDepBra(0,t)
assert k.subs(t,2) == TimeDepKet(0,2)
k = TimeDepKet(x, 0.5)
assert k.label == (x,)
assert k.args == (x,sympify(0.5))
def test_time_dep_ket():
k = TimeDepKet(0, t)
assert isinstance(k, TimeDepKet)
assert isinstance(k, KetBase)
assert isinstance(k, StateBase)
assert isinstance(k, QExpr)
assert k.label == (Integer(0),)
assert k.args == (Integer(0), t)
assert k.time == t
assert k.dual_class() == TimeDepBra
assert k.dual == TimeDepBra(0, t)
assert k.subs(t, 2) == TimeDepKet(0, 2)
k = TimeDepKet(x, 0.5)
assert k.label == (x,)
assert k.args == (x, sympify(0.5))
k = CustomTimeDepKet()
assert k.label == (Symbol("test"),)
assert k.time == Symbol("t")
assert k == CustomTimeDepKet("test", "t")
k = CustomTimeDepKetMultipleLabels()
assert k.label == (Symbol("r"), Symbol("theta"), Symbol("phi"))
assert k.time == Symbol("t")
assert k == CustomTimeDepKetMultipleLabels("r", "theta", "phi", "t")
assert TimeDepKet() == TimeDepKet("psi", "t")
def test_time_dep_bra():
b = TimeDepBra(0, t)
assert isinstance(b, TimeDepBra)
assert isinstance(b, BraBase)
assert isinstance(b, StateBase)
assert isinstance(b, QExpr)
assert b.label == (Integer(0), )
assert b.args == (Integer(0), t)
assert b.time == t
assert b.dual_class == TimeDepKet
assert b.dual == TimeDepKet(0, t)
k = TimeDepBra(x, 0.5)
assert k.label == (x, )
assert k.args == (x, sympify(0.5))
def test_time_dep_ket():
k = TimeDepKet(0, t)
assert isinstance(k, TimeDepKet)
assert isinstance(k, KetBase)
assert isinstance(k, StateBase)
assert isinstance(k, QExpr)
assert k.label == (Integer(0), )
assert k.args == (Integer(0), t)
assert k.time == t
assert k.dual_class == TimeDepBra
assert k.dual == TimeDepBra(0, t)
assert k.subs(t, 2) == TimeDepKet(0, 2)
k = TimeDepKet(x, 0.5)
assert k.label == (x, )
assert k.args == (x, sympify(0.5))
def test_sympy__physics__quantum__state__TimeDepKet():
from sympy.physics.quantum.state import TimeDepKet
assert _test_args(TimeDepKet('psi', 't'))
def test_state():
x = symbols('x')
bra = Bra()
ket = Ket()
bra_tall = Bra(x / 2)
ket_tall = Ket(x / 2)
tbra = TimeDepBra()
tket = TimeDepKet()
assert str(bra) == '<psi|'
assert pretty(bra) == '<psi|'
assert upretty(bra) == u'⟨ψ❘'
assert latex(bra) == r'{\left\langle \psi\right|}'
sT(bra, "Bra(Symbol('psi'))")
assert str(ket) == '|psi>'
assert pretty(ket) == '|psi>'
assert upretty(ket) == u'❘ψ⟩'
assert latex(ket) == r'{\left|\psi\right\rangle }'
sT(ket, "Ket(Symbol('psi'))")
assert str(bra_tall) == '<x/2|'
ascii_str = \
"""\
/ |\n\
/ x|\n\
\\ -|\n\
\\2|\
"""
ucode_str = \
u"""\
╱ │\n\
╱ x│\n\
╲ ─│\n\
╲2│\
"""
assert pretty(bra_tall) == ascii_str
assert upretty(bra_tall) == ucode_str
assert latex(bra_tall) == r'{\left\langle \frac{1}{2} x\right|}'
sT(bra_tall, "Bra(Mul(Rational(1, 2), Symbol('x')))")
assert str(ket_tall) == '|x/2>'
ascii_str = \
"""\
| \\ \n\
|x \\\n\
|- /\n\
|2/ \
"""
ucode_str = \
u"""\
│ ╲ \n\
│x ╲\n\
│─ ╱\n\
│2╱ \
"""
assert pretty(ket_tall) == ascii_str
assert upretty(ket_tall) == ucode_str
assert latex(ket_tall) == r'{\left|\frac{1}{2} x\right\rangle }'
sT(ket_tall, "Ket(Mul(Rational(1, 2), Symbol('x')))")
assert str(tbra) == '<psi;t|'
assert pretty(tbra) == u'<psi;t|'
assert upretty(tbra) == u'⟨ψ;t❘'
assert latex(tbra) == r'{\left\langle \psi;t\right|}'
sT(tbra, "TimeDepBra(Symbol('psi'),Symbol('t'))")
assert str(tket) == '|psi;t>'
assert pretty(tket) == '|psi;t>'
assert upretty(tket) == u'❘ψ;t⟩'
assert latex(tket) == r'{\left|\psi;t\right\rangle }'
sT(tket, "TimeDepKet(Symbol('psi'),Symbol('t'))")
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_time_dep_ket():
k = TimeDepKet(0, t)
assert isinstance(k, TimeDepKet)
assert isinstance(k, KetBase)
assert isinstance(k, StateBase)
assert isinstance(k, QExpr)
assert k.label == (Integer(0), )
assert k.args == (Integer(0), t)
assert k.time == t
assert k.dual_class() == TimeDepBra
assert k.dual == TimeDepBra(0, t)
assert k.subs(t, 2) == TimeDepKet(0, 2)
k = TimeDepKet(x, 0.5)
assert k.label == (x, )
assert k.args == (x, sympify(0.5))
k = CustomTimeDepKet()
assert k.label == (Symbol("test"), )
assert k.time == Symbol("t")
assert k == CustomTimeDepKet("test", "t")
k = CustomTimeDepKetMultipleLabels()
assert k.label == (Symbol("r"), Symbol("theta"), Symbol("phi"))
assert k.time == Symbol("t")
assert k == CustomTimeDepKetMultipleLabels("r", "theta", "phi", "t")
assert TimeDepKet() == TimeDepKet("psi", "t")
def test_state():
x = symbols("x")
bra = Bra()
ket = Ket()
bra_tall = Bra(x / 2)
ket_tall = Ket(x / 2)
tbra = TimeDepBra()
tket = TimeDepKet()
assert str(bra) == "<psi|"
assert pretty(bra) == "<psi|"
assert upretty(bra) == u"⟨ψ❘"
assert latex(bra) == r"{\left\langle \psi\right|}"
sT(bra, "Bra(Symbol('psi'))")
assert str(ket) == "|psi>"
assert pretty(ket) == "|psi>"
assert upretty(ket) == u"❘ψ⟩"
assert latex(ket) == r"{\left|\psi\right\rangle }"
sT(ket, "Ket(Symbol('psi'))")
assert str(bra_tall) == "<x/2|"
ascii_str = """\
/ |\n\
/ x|\n\
\\ -|\n\
\\2|\
"""
ucode_str = u("""\
╱ │\n\
╱ x│\n\
╲ ─│\n\
╲2│\
""")
assert pretty(bra_tall) == ascii_str
assert upretty(bra_tall) == ucode_str
assert latex(bra_tall) == r"{\left\langle \frac{x}{2}\right|}"
sT(bra_tall, "Bra(Mul(Rational(1, 2), Symbol('x')))")
assert str(ket_tall) == "|x/2>"
ascii_str = """\
| \\ \n\
|x \\\n\
|- /\n\
|2/ \
"""
ucode_str = u("""\
│ ╲ \n\
│x ╲\n\
│─ ╱\n\
│2╱ \
""")
assert pretty(ket_tall) == ascii_str
assert upretty(ket_tall) == ucode_str
assert latex(ket_tall) == r"{\left|\frac{x}{2}\right\rangle }"
sT(ket_tall, "Ket(Mul(Rational(1, 2), Symbol('x')))")
assert str(tbra) == "<psi;t|"
assert pretty(tbra) == u"<psi;t|"
assert upretty(tbra) == u"⟨ψ;t❘"
assert latex(tbra) == r"{\left\langle \psi;t\right|}"
sT(tbra, "TimeDepBra(Symbol('psi'),Symbol('t'))")
assert str(tket) == "|psi;t>"
assert pretty(tket) == "|psi;t>"
assert upretty(tket) == u"❘ψ;t⟩"
assert latex(tket) == r"{\left|\psi;t\right\rangle }"
sT(tket, "TimeDepKet(Symbol('psi'),Symbol('t'))")