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## Homework Statement

Given [itex]\nabla\frac{1}{r}[/itex], show [itex]\nabla\bullet\nabla\frac{1}{r}[/itex] = -4πδ(r), where δ(r) is the delta dirac function.

## The Attempt at a Solution

I've used divergence theorem and also solved the equation itself, so I know that outright solving is zero and the divergence theorem gives -4π. But I'm not sure how to show the presence, or rather, how I get the delta dirac function. I understand its role and but not necessarily why it needs to be there. Any help on direction on this one would be greatly appreciated.