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"""Tests for sho1d.py"""
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.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')
a_rep = represent(a, basis=N, ndim=4, format='sympy')
N_rep = represent(N, basis=N, ndim=4, format='sympy')
H_rep = represent(H, basis=N, ndim=4, format='sympy')
k3_rep = represent(k3, basis=N, ndim=4, format='sympy')
b3_rep = represent(b3, basis=N, ndim=4, format='sympy')
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)
for i in range(ndim - 1):
assert a_rep[i,i + 1] == sqrt(i + 1)
def test_NumberOp():
assert Commutator(N, ad).doit() == ad
assert Commutator(N, a).doit() == Integer(-1)*a
assert Commutator(N, H).doit() == Integer(0)
assert qapply(N*k) == (k.n*k).expand()
assert N.rewrite('a').doit() == ad*a
assert N.rewrite('xp').doit() == (Integer(1)/(Integer(2)*m*hbar*omega))*(
Px**2 + (m*omega*X)**2) - Integer(1)/Integer(2)
assert N.rewrite('H').doit() == H/(hbar*omega) - Integer(1)/Integer(2)
for i in range(ndim):
assert N_rep[i,i] == i
assert N_rep == ad_rep_sympy*a_rep
def test_Hamiltonian():
assert Commutator(H, N).doit() == Integer(0)
assert qapply(H*k) == ((hbar*omega*(k.n + Integer(1)/Integer(2)))*k).expand()
assert H.rewrite('a').doit() == hbar*omega*(ad*a + Integer(1)/Integer(2))
assert H.rewrite('xp').doit() == \
(Integer(1)/(Integer(2)*m))*(Px**2 + (m*omega*X)**2)
assert H.rewrite('N').doit() == hbar*omega*(N + Integer(1)/Integer(2))
for i in range(ndim):
assert H_rep[i,i] == hbar*omega*(i + Integer(1)/Integer(2))
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)
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