What is the Eigenvalue Equation for a 2D Harmonic Oscillator?

[shally]

Homework Statement

Please take a look at the attachment for the problem statement.

Homework Equations

For 1 dim Harmonic oscillator, E = (n+1/2)h.omega/2pi

I don't know which equation to use for 2 dim

The Attempt at a Solution

I am unable to solve because I don't know which equation to apply. Kindly help.

 

[vela]

You plug the potential into the Schrodinger equation and solve for the eigenvalues and eigenfunctions.

 

[ehild]

The two-dimensional oscillator can be considered as two independent one-dimensional ones, according to the potential function (x and y are not mixed). Both oscillators have eigenvalues in the form of hf(n+1/2). (f is the frequency of the oscillator). You can see from the potential function how the oscillator frequencies are related. The energy of the oscillator is the sum of the one-dimensional energy eigenvalues.

ehild