%load_ext sympy.interactive.ipythonprinting 
from sympy import *
from IPython.display import display_pretty
from sympy.physics.quantum import *
from sympy.physics.quantum.sho1d import *
from sympy.physics.quantum.tests.test_sho1d import *

ad = RaisingOp('a')
a = LoweringOp('a')

ad

a

print latex(ad)
print latex(a)

display_pretty(ad)
display_pretty(a)

print srepr(ad)
print srepr(a)

print repr(ad)
print repr(a)

k = SHOKet('k')
b = SHOBra('b')

k

b

print pretty(k)
print pretty(b)

print latex(k)
print latex(b)

print srepr(k)
print srepr(b)

Dagger(ad)

Dagger(a)

Commutator(ad,a).doit()

Commutator(a,ad).doit()

k.dual

b.dual

InnerProduct(b,k).doit()

qapply(ad*k)

qapply(a*k)

kg = SHOKet(0)
kf = SHOKet(1)

qapply(ad*kg)

qapply(ad*kf)

qapply(a*kg)

qapply(a*kf)

k = SHOKet('k')
ad = RaisingOp('a')
a = LoweringOp('a')
N = NumberOp('N')
H = Hamiltonian('H')

N().rewrite('a').doit()

N().rewrite('xp').doit()

N().rewrite('H').doit()

H().rewrite('a').doit()

H().rewrite('xp').doit()

H().rewrite('N').doit()

ad().rewrite('xp').doit()

a().rewrite('xp').doit()

qapply(N*k)

ks = SHOKet(2)
qapply(N*ks)

qapply(H*k)

Commutator(N,ad).doit()

Commutator(N,a).doit()

Commutator(N,H).doit()

represent(ad, basis=N, ndim=4, format='sympy')

represent(ad, basis=N, ndim=5, format='numpy')

represent(ad, basis=N, ndim=4, format='scipy.sparse', spmatrix='lil')

print represent(ad, basis=N, ndim=4, format='scipy.sparse', spmatrix='lil')

represent(a, basis=N, ndim=4, format='sympy')

represent(N, basis=N, ndim=4, format='sympy')

represent(H, basis=N, ndim=4, format='sympy')

k0 = SHOKet(0)
k1 = SHOKet(1)
b0 = SHOBra(0)
b1 = SHOBra(1)

print represent(k0, basis=N, ndim=5, format='sympy')

print represent(k1, basis=N, ndim=5, format='sympy')

print represent(b0, basis=N, ndim=5, format='sympy')

print represent(b1, basis=N, ndim=5, format='sympy')