Differential equation in Annulus

[FedEx]

Hi,

I want to solve a differential equation which goes like this..

$\nabla^{2}\psi = A\psi$

For an annulus having inner diameter as a and outer diameter as b. (A is some constant)

I can write down the laplacian in polar co-ordinates and carry on and get a bessel function as the solution.. And then apply the boundary conditions that at r=a and r=b $\psi = 0$

Will this do? Or will i have to incorporate the structure of the annulus in the equation like making a co-ordinate transform from r to r-a etc..

 

[HallsofIvy]

What you say you are doing is perfectly correct.