# Homework Help: Eigenvalue problem

1. May 2, 2010

### isison

[URGENT] Eigenvalue problem

1. The problem statement, all variables and given/known data
[PLAIN]http://img228.imageshack.us/img228/4990/111em.png [Broken]

2. Relevant equations
Sturm-Liouville equation?

3. The attempt at a solution
I guess I'm just totally lost here. I've no idea how to start. It seems to me that maybe solving for solutions directly is ok, but that's near impossible in this case. I think there's some clever way around.

Last edited by a moderator: May 4, 2017
2. May 2, 2010

### vela

Staff Emeritus
Re: [URGENT] Eigenvalue problem

Plug f(x) into the eigenvalue equation and use the Laplacian in spherical coordinates in n dimensions to expand the lefthand side.

3. May 2, 2010

### isison

Re: [URGENT] Eigenvalue problem

Thanks!

How about g(x)? How do I prove g(x) is also a solution?

4. May 2, 2010

### vela

Staff Emeritus
Re: [URGENT] Eigenvalue problem

Same way, I'd imagine.

5. May 2, 2010

### isison

Re: [URGENT] Eigenvalue problem

Well, I tried to do the same thing, but I just can't reach the same conclusion. Where does k come from? How do I get that term with k?

Thanks,

6. May 2, 2010

### vela

Staff Emeritus
Re: [URGENT] Eigenvalue problem

It should come from the Laplacian acting on the spherical harmonic.