2.3 Find the eigenvalues and vectors of J $_\theta$ for $\theta$ =45¶

from qutip import *
from numpy import cos, sin, pi, deg2rad

qm = Qobj([[cos(pi/4)**2,cos(pi/4)*sin(pi/4)],[cos(pi/4)*sin(pi/4),sin(pi/4)**2]])

qm

qm.eigenstates()

(array([0., 1.]),
 array([Quantum object: dims=[[2], [1]], shape=(2, 1), type='ket', dtype=Dense
        Qobj data =
        [[ 0.70710678]
         [-0.70710678]]                                                       ,
        Quantum object: dims=[[2], [1]], shape=(2, 1), type='ket', dtype=Dense
        Qobj data =
        [[-0.70710678]
         [-0.70710678]]                                                       ],
       dtype=object))

from numpy import sqrt, exp
1/sqrt(2)

np.float64(0.7071067811865475)

phi = 1.5
Jphi = Qobj([[exp(1j)*phi,0],[0,1]])
Jphi

hvec = Qobj([[1],[0]])
hvec

vvec = Qobj([[0],[1]])
vvec

Jphi*hvec

Jphi*vvec

2.3 Find the eigenvalues and vectors of J_\theta for \theta=45

2.3 Find the eigenvalues and vectors of Jθ_\thetaθ​ for θ\thetaθ=45¶

2.3 Find the eigenvalues and vectors of J $_\theta$ for $\theta$ =45¶