# PDE of a function of two variables (cylindrical coordinates with azimuthal symmetry)

1. Dec 10, 2011

### mtszyk

1. The problem statement, all variables and given/known data
Solve in cylindrical coordinates
$-m\delta(z)\delta(\rho-a)=\partial^2_z A(z,\rho)+\partial^2_\rho A(z,\rho)+\frac{1}{\rho}\partial_\rho A(z,\rho)-\frac{1}{\rho^2}A(z,\rho)$

Where $\partial_i$ is the partial derivative with respect to $i$.

2. Relevant equations
It is suggested to use an integral representation for a delta function (only for the $\rho$ delta), which I think is:
$\delta(\rho-a)=\frac{1}{2 \pi}\int_{-\infty}^{\infty}e^{i k (\rho-a)}\,\mathrm{d}k$

But it could refer to a representation using bessel functions, because I expect there to be bessel functions in the answer.

3. The attempt at a solution
My first attempt went with assuming that because there is delta functions, I can initially set those equal to zero and use the separation of variables, and expect the final answer to be in the form of whatever I get. Turns out that doesn't quite work.

Now I'm a bit lost, anyone have a direction to point me in?