# Homework Help: Quantum Harmonic Oscillator

1. Nov 2, 2011

### atomicpedals

1. The problem statement, all variables and given/known data

Consider the Hamiltonian

$$H=\frac{p^2}{2M}+\frac{1}{2}\omega^2r^2-\omega_z L_z$$

Determine its eigenstates and energies.

2. The attempt at a solution

I want to check my comprehension; by eigenstate they mean

$$\psi(r)$$
from the good old

$$H\psi(r)=E\psi(r)$$
and then the energies would then be solutions for E?

2. Nov 2, 2011

### atomicpedals

To sort of answer my own question the eigenstates would more properly probably be
$$|\psi>$$
in
$$H|\psi>=E|\psi>$$

3. Nov 2, 2011

### vela

Staff Emeritus
It's a three-dimensional problem, so the wave function will be a function of r, θ, and φ.

4. Nov 2, 2011

### atomicpedals

Ah, right. (and just as I was getting comfortable in 2D)

5. Nov 3, 2011

### dextercioby

Convert L_z and p to spherical coordinates and separate variables just like in the H-atom case, or the isotropic 3D oscillator.