Homework Help: 3-dimensional harmonic oscillator (quantum mechanics)

1. Apr 28, 2009

Kruum

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

3-dimensional harmonic oscillator has a potetnial energy of $$U(x,y,z)=\frac{1}{2}k'(x^2+y^2+z^2)$$.
a) Determine the energy levels of the oscillator as a function of angular velocity.
b) Calculate the value for the ground state energy and the separation between adjacent energy levels.

2. Relevant equations

$$-\frac{\hbar^2}{2m}\nabla ^2\psi+U\psi=E\psi$$

3. The attempt at a solution

We have a wave function $$\psi=\psi(x,y,z)$$. I plug it in the equation and get nothing that helps me, since I don't know the function. Any suggestions?