def test_RaisingOp():
assert Dagger(ad) == a
assert Commutator(ad, a).doit() == Integer(-1)
assert Commutator(ad, N).doit() == Integer(-1) * ad
assert qapply(ad * k) == (sqrt(k.n + 1) * SHOKet(k.n + 1)).expand()
assert qapply(ad * kz) == (sqrt(kz.n + 1) * SHOKet(kz.n + 1)).expand()
assert qapply(ad * kf) == (sqrt(kf.n + 1) * SHOKet(kf.n + 1)).expand()
assert ad.rewrite('xp').doit() == \
(Integer(1)/sqrt(Integer(2)*hbar*m*omega))*(Integer(-1)*I*Px + m*omega*X)
assert ad.hilbert_space == ComplexSpace(S.Infinity)
for i in range(ndim - 1):
assert ad_rep_sympy[i + 1, i] == sqrt(i + 1)
if not np:
skip("numpy not installed.")
ad_rep_numpy = represent(ad, basis=N, ndim=4, format='numpy')
for i in range(ndim - 1):
assert ad_rep_numpy[i + 1, i] == float(sqrt(i + 1))
if not np:
skip("numpy not installed.")
if not scipy:
skip("scipy not installed.")
ad_rep_scipy = represent(ad,
basis=N,
ndim=4,
format='scipy.sparse',
spmatrix='lil')
for i in range(ndim - 1):
assert ad_rep_scipy[i + 1, i] == float(sqrt(i + 1))
assert ad_rep_numpy.dtype == 'float64'
assert ad_rep_scipy.dtype == 'float64'
def test_LoweringOp():
assert Dagger(a) == ad
assert Commutator(a, ad).doit() == Integer(1)
assert Commutator(a, N).doit() == a
assert qapply(a * k) == (sqrt(k.n) * SHOKet(k.n - Integer(1))).expand()
assert qapply(a * kz) == Integer(0)
assert qapply(a * kf) == (sqrt(kf.n) * SHOKet(kf.n - Integer(1))).expand()
assert a().rewrite('xp').doit() == \
(Integer(1)/sqrt(Integer(2)*hbar*m*omega))*(I*Px + m*omega*X)
def test_RaisingOp():
assert Dagger(ad) == a
assert Commutator(ad, a).doit() == Integer(-1)
assert Commutator(ad, N).doit() == Integer(-1) * ad
assert qapply(ad * k) == (sqrt(k.n + 1) * SHOKet(k.n + 1)).expand()
assert qapply(ad * kz) == (sqrt(kz.n + 1) * SHOKet(kz.n + 1)).expand()
assert qapply(ad * kf) == (sqrt(kf.n + 1) * SHOKet(kf.n + 1)).expand()
assert ad().rewrite('xp').doit() == \
(Integer(1)/sqrt(Integer(2)*hbar*m*omega))*(Integer(-1)*I*Px + m*omega*X)
assert ad.hilbert_space == ComplexSpace(S.Infinity)
def test_LoweringOp():
assert Dagger(a) == ad
assert Commutator(a, ad).doit() == Integer(1)
assert Commutator(a, N).doit() == a
assert qapply(a * k) == (sqrt(k.n) * SHOKet(k.n - Integer(1))).expand()
assert qapply(a * kz) == Integer(0)
assert qapply(a * kf) == (sqrt(kf.n) * SHOKet(kf.n - Integer(1))).expand()
assert a.rewrite("xp").doit() == (
Integer(1) / sqrt(Integer(2) * hbar * m * omega)
) * (I * Px + m * omega * X)
for i in range(ndim - 1):
assert a_rep[i, i + 1] == sqrt(i + 1)
def test_SHOKet():
assert SHOKet('k').dual_class() == SHOBra
assert SHOBra('b').dual_class() == SHOKet
assert InnerProduct(b, k).doit() == KroneckerDelta(k.n, b.n)
assert k.hilbert_space == ComplexSpace(S.Infinity)
assert k3_rep[k3.n, 0] == Integer(1)
assert b3_rep[0, b3.n] == Integer(1)
from sympy.physics.quantum import Commutator
from sympy.physics.quantum.qapply import qapply
from sympy.physics.quantum.innerproduct import InnerProduct
from sympy.physics.quantum.cartesian import X, Px
from sympy.functions.special.tensor_functions import KroneckerDelta
from sympy.physics.quantum.hilbert import ComplexSpace
from sympy.physics.quantum.represent import represent
from sympy.external import import_module
from sympy.testing.pytest import skip
from sympy.physics.quantum.sho1d import (RaisingOp, LoweringOp, SHOKet, SHOBra,
Hamiltonian, NumberOp)
ad = RaisingOp('a')
a = LoweringOp('a')
k = SHOKet('k')
kz = SHOKet(0)
kf = SHOKet(1)
k3 = SHOKet(3)
b = SHOBra('b')
b3 = SHOBra(3)
H = Hamiltonian('H')
N = NumberOp('N')
omega = Symbol('omega')
m = Symbol('m')
ndim = Integer(4)
np = import_module('numpy')
scipy = import_module('scipy', __import__kwargs={'fromlist': ['sparse']})
ad_rep_sympy = represent(ad, basis=N, ndim=4, format='sympy')
def test_SHOKet():
assert SHOKet('k').dual_class() == SHOBra
assert SHOBra('b').dual_class() == SHOKet
assert InnerProduct(b, k).doit() == KroneckerDelta(k.n, b.n)
assert k.hilbert_space == ComplexSpace(S.Infinity)
from sympy import Integer, Symbol, sqrt, I, S
from sympy.physics.quantum import Dagger
from sympy.physics.quantum.constants import hbar
from sympy.physics.quantum import Commutator
from sympy.physics.quantum.qapply import qapply
from sympy.physics.quantum.innerproduct import InnerProduct
from sympy.physics.quantum.cartesian import X, Px
from sympy.functions.special.tensor_functions import KroneckerDelta
from sympy.physics.quantum.hilbert import ComplexSpace
from sympy.physics.quantum.sho1d import (RaisingOp, LoweringOp, SHOKet, SHOBra,
Hamiltonian, NumberOp)
ad = RaisingOp('a')
a = LoweringOp('a')
k = SHOKet('k')
kz = SHOKet(0)
kf = SHOKet(1)
b = SHOBra('b')
H = Hamiltonian('H')
N = NumberOp('N')
omega = Symbol('omega')
m = Symbol('m')
def test_RaisingOp():
assert Dagger(ad) == a
assert Commutator(ad, a).doit() == Integer(-1)
assert Commutator(ad, N).doit() == Integer(-1) * ad
assert qapply(ad * k) == (sqrt(k.n + 1) * SHOKet(k.n + 1)).expand()
assert qapply(ad * kz) == (sqrt(kz.n + 1) * SHOKet(kz.n + 1)).expand()
from sympy.physics.quantum.represent import represent
from sympy.external import import_module
from sympy.testing.pytest import skip
from sympy.physics.quantum.sho1d import (
RaisingOp,
LoweringOp,
SHOKet,
SHOBra,
Hamiltonian,
NumberOp,
)
ad = RaisingOp("a")
a = LoweringOp("a")
k = SHOKet("k")
kz = SHOKet(0)
kf = SHOKet(1)
k3 = SHOKet(3)
b = SHOBra("b")
b3 = SHOBra(3)
H = Hamiltonian("H")
N = NumberOp("N")
omega = Symbol("omega")
m = Symbol("m")
ndim = Integer(4)
np = import_module("numpy")
scipy = import_module("scipy", import_kwargs={"fromlist": ["sparse"]})
ad_rep_sympy = represent(ad, basis=N, ndim=4, format="sympy")
