# Eigenstate for a 3D harmonic oscillator

1. Oct 11, 2012

### JordanGo

1. The problem statement, all variables and given/known data
A 3D harmonic oscillator has the following potential:

$V(x,y,z) = \frac{1}{2}m( \varpi_{x}^2x^2 + \varpi_{y}^2y^2 + \varpi_{z}^2z^2)$

Find the energy eigenstates and energy eigenvalues for this system.

3. The attempt at a solution

I found the energy eigenvalue to be:

$E = E_{x} + E_{y} + E_{z}$

$E = \hbar((n_{x}+\frac{1}{2})\varpi_{x} + (n_{y}+\frac{1}{2})\varpi_{y} + (n_{z}+\frac{1}{2})\varpi_{z})$

Now I know that the eigenstate is:

$\Psi = \Psi_{x} \times \Psi_{y} \times \Psi_{z}$

But I don't know how to find ψx, ψy or ψz.

Can someone help me?

2. Oct 12, 2012

### PhysicsGente

Hey JordanGo.
Try writing down your 3-D Schrödinger equation and use separation of variables.

3. Oct 12, 2012

### vela

Staff Emeritus
How did you find the energy eigenvalues? It seems to me if you can figure those out correctly, it's pretty straightforward to see how to get the eigenstates. Show your work so far.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook