Lab 8 - Simple Harmonic Oscillator states

Problems from Chapter 12

from numpy import sqrt
from qutip import *

Define the standard operators¶

N = 10  # pick a size for our state-space
a = destroy(N)
n = a.dag()*a

Problem 12.1:¶

a*a.dag() - a.dag()*a

Problem 12.2:¶

n*a.dag() - a.dag()*n

n*a.dag() - a.dag()*n == a.dag()

Problem 12.3 (use n=2 as a test-case):¶

To define $|2\rangle$ use the basis(N,n) command where N is the dimension of the vector, and n is the quantum number.

psi = basis(N,2)

Problem 12.5 and 12.6:¶

These are simple, just view the matrix representation of the operators

Problem 12.7:¶

First, define $\hat{X}$ and $\hat{P}$ operators

X=
P=

psi = 1/sqrt(2)*(basis(N,1)+basis(N,2))

Problem 12.8:¶

psi = 1/sqrt(2)*(basis(N,2)+basis(N,4))