from sympy.physics.quantum import *
from sympy.physics.cartesian import *
from sympy.physics.piab import *
from sympy.physics.spin import *

# Basic manipulations with operators, bras, kets and commutators

psi, phi = Ket('psi'), Ket('phi')
psi, phi
A, B, C = Operator('A'), Operator('B'), Operator('C')
Dagger(phi)*Commutator(2*A+B,I*C)*psi
_.expand(commutator=True)  # '_' = last result
_.doit().expand()
Dagger(_)

# Basic 1D position and momentum

Commutator(X, Px)
_.doit()
Commutator(X, X)
X**2*XKet('y')
apply_operators(_)
XBra('xp')*XKet('x')
_.doit()

# The 1D PIAB

H = PIABHamiltonian('H')
boxket = PIABKet('n')
H*boxket
apply_operators(_)
represent(boxket, X)

# Spin commutation relations and operator identities

Commutator(Jx, Jy)
_.doit()
Commutator(J2, Jz)
_.doit()
Dagger(Jx), Dagger(Jy), Dagger(Jz)
J2.rewrite('plusminus')

# A crazy tensor product representation


H = TensorProduct(Jx,Jx)+TensorProduct(Jy,Jy)+TensorProduct(Jz, Jz)
H
represent(H, Jz, j=Rational(1,2))

# Applying spin operators and looking at R

k = JzKet(('j','m'))
Jx*k
apply_operators(_)
Jplus*Jminus*k
apply_operators(_)

# Rotation operator

R = Rotation((0, pi/2, 0))  # Rotation operator (Wigner D-Function)
R
represent(R, Jz, j=Rational(1,2))  # Represent for j=1/2
represent(R, Jz, j=1)              # Now for j=1