Homework Help: Green's Function

1. Nov 27, 2012

the_kid

1. The problem statement, all variables and given/known data

I'm trying to show that the Green's function for the Laplace operator $-\nabla^2$ is badly behaved at infinity. I.e.

$$\int d^dx|G(x,y)|^2=\infty$$ for d=1,2,3. What happens when d>4?

I know the 1D Green's function is given by

$$G(x,y)=-\frac{|x-y|}{2}$$

2. Relevant equations

3. The attempt at a solution

$$G(x,y)\propto|x-y|^{-(d-2)}$$ for d>2

I need to be able to show that the above integral diverges...