- #1
davidbenari
- 466
- 18
Homework Statement
Prove that ##(x^2+y^2+z^2)\nabla^2[\delta(x)\delta(y)\delta(z)]=6\delta(x)\delta(y)\delta(z)##
Homework Equations
##\delta''(x)/2=\delta(x)/x^2##
The Attempt at a Solution
I have obtained this:
##6\delta(x)\delta(y)\delta(z) + (xy)^2/2\Bigg(\delta''(y)\delta''(z)+\delta''(x)\delta''(z)\Bigg)+(xz)^2/2\Bigg(\delta''(y)\delta''(z)+\delta''(x)\delta''(y)\Bigg)+(yz)^2/2\Bigg(\delta''(x)\delta''(z)+\delta''(x)\delta''(y)\Bigg)##
This looks like a huge mess, hehe, sorry.
Any ideas on how to make disappear those ugly terms and only remain with the first one?
Thanks.