Two dimensional asymmetric harmonic oscillator

[JackPunchedJi]

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

Homework Statement

The potential is of course defined by: V = 1/2m(Omegax)x^2 + 1/2m(Omegay)y^2

Homework 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?

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.

 

[fzero]

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