# Homework Help: Two dimensional asymmetric harmonic oscillator

1. Mar 12, 2012

### JackPunchedJi

Let's say I have a 2D harmonic oscillator:

1. The problem statement, all variables and given/known data
The potential is of course defined by: V = 1/2m(Omegax)x^2 + 1/2m(Omegay)y^2

2. Relevant equations

Generally when doing a harmonic oscillator we find that in two dimensions the energy is just:

(Nx+Ny+1)hbarOmega is the energy.

How does this change when the Omegax and Omegay are not equal?

3. The attempt at a solution

Do we simply get the energy as...

E = (Nx+1/2)hbarOmegax + (Ny+1/2)hhbarOmegay ?

That would seem logical, but would like the clarification.

2. Mar 12, 2012

### fzero

Your intuition is correct. You can work it out by considering a separable solution of the form $\psi(x,y)= X(x)Y(y)$.