In [1]:

    

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


    

In [2]:

    

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


    

In [3]:

    

qm


    

    
Out[3]:





Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.500 & 0.500\\0.500 & 0.500\\\end{array}\right)\end{equation*}

In [4]:

    

qm.eigenstates()


    

    
Out[4]:





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

In [5]:

    

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


    

    
Out[5]:





0.70710678118654746

In [6]:

    

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


    

    
Out[6]:





Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}(0.810+1.262j) & 0.0\\0.0 & 1.0\\\end{array}\right)\end{equation*}

In [7]:

    

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


    

    
Out[7]:





Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\begin{equation*}\left(\begin{array}{*{11}c}1.0\\0.0\\\end{array}\right)\end{equation*}

In [8]:

    

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


    

    
Out[8]:





Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\begin{equation*}\left(\begin{array}{*{11}c}0.0\\1.0\\\end{array}\right)\end{equation*}

In [9]:

    

Jphi*hvec


    

    
Out[9]:





Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\begin{equation*}\left(\begin{array}{*{11}c}(0.810+1.262j)\\0.0\\\end{array}\right)\end{equation*}

In [10]:

    

Jphi*vvec


    

    
Out[10]:





Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\begin{equation*}\left(\begin{array}{*{11}c}0.0\\1.0\\\end{array}\right)\end{equation*}

In [ ]: