Solving Poissons equation with a delta function in RHS using separation of variables.

Hi Everyone,

I am trying to solve the partial differential equation given below:

$\displaystyle \Delta^2\phi(x,y,z)=\frac{qf(x,y,z)}{\epsilon}$

where $\displaystyle f(x,y,z)=1$ at one point and zero elsewhere.

This is the poisons equation for a point charge inside a conducting box.

Can this be solved using the variable separable method?

When I work through it I get:

$\displaystyle \frac{1}{X(x)}\frac{d^2X(x)}{dx^2}+\frac{1}{Y(y)} \frac{d^2Y(y)}{dy^2}+\frac{1}{Z(z)}\frac{d^2Z(z)}{ dz^2}=\frac{qf(x,y,z)}{\epsilon X(x)Y(y)Z(z)}$

If this cannot be solved using this method? What others methods can I use. If some one can give me a reference I am thankful.