Why does the following function equate to a delta in classical feild theory

[Fwahnak]

Homework Statement

Can anyone remember a decent argument/derivation for the following representation of the delta function.

Homework Equations

$ \nabla^2 \frac{1}{|r|} =\delta(r)$

(probally up to some multipicative constant $\frac{1}{2\pi}$ or something

The Attempt at a Solution

I know I've seen an agrument in jackson but I don't have a copy.

 

[Fwahnak]

I've no confidence that I've latexed that correctly and my work computer won't show me the symbols so here's the equation in equation again

div(grad(1/|r|)) is proportional to deltafunction(r)