# Quantum Harmonic Oscillator

## Homework Statement

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?

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

vela
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