Suppose we have a 2D harmonic oscillator in the state
|psi :
a. What is the expectation value of the operator hat(L)_(z)=ℏ(hat(a)_(1)^(†)hat(a)_(1)-hat(a)_(2)^(†)hat(a)_(2)) ?
b. What is the expectation value of the energy?
Hint: Recall that
hat(a)_(1)=(1)/(sqrt(2))(hat(a)_(x)-ihat(a)_(y))
hat(a)_(2)=(1)/(sqrt(2))(hat(a)_(x)+ihat(a)_(y)).
7. Suppose we have a 2D harmonic oscillator in the state
nx=0,n=2)
a. What is the expectation value of the operator Lz = h (aa - aa2)? b. What is the expectation value of the energy?
Hint: Recall that
1 : V2 1 a2 (@x+iay)