What is the General Solution for the Schrödinger Equation in a 2D or 3D Box?

[kasse]

The solution of the one dimensional Schrödinger equation for a particle in a one dimensional box is $$Asin \frac{n \pi x}{a}$$. But how about if the box is 2D or 3D?

 

[gabbagabbahey]

Have you considered actually solving the Schroedinger equation for these cases?...An attempt at that would probably be a good way to start.

 

[kasse]

What is the general solution then?

 

[gabbagabbahey]

What is the general solution then?

Show us an attempt and I'll be happy to help you. Start with the 2D case.