How can I prove Helmholtz' Theorem using spherical coordinates?

[parksy7]

Hi everyone, new to this site and was wondering if anyone could help me out...

I am trying to prove the following equation to be true but don't really know where to start. Supposedly, I should be finding the Laplacian first using spherical coordinates.

∇^2(1/|R|) = -4*pi*δ(R)

where |R|= |r-r'| and R = r-r'

and δ(R) = δ(r-r') = δ(x-x')δ(y-y')δ(z-z')

I realize this is a mess with how it looks, but wasn't sure how to convert mathematica text into the thread window.

Thanks for any help!

 

[Galileo]

Try using the divergence theorem. Can you show what you got so far?