# Question on using solution from Helmholtz equation in Poisson equation

1. Nov 21, 2013

### yungman

Helmholtz equation stated that
$$\nabla^2 u(r,\theta,\phi) =-ku(r,\theta,\phi) = f(r,\theta,\phi)$$
This is being used for Poisson equation with zero boundary:
$$\nabla^2 u(r,\theta,\phi) = f(r,\theta,\phi)$$
and
$$u(a,\theta,\phi)=0$$

I just don't see how this can work as $k=m^2$ is a number only.

If $\nabla^2 u(r,\theta,\phi)=1$ which means $ku(r,\theta,\phi)$ is only constant numbers depending on $m$!!!

If $u(r,\theta,\phi)$ is a constant number only, that cannot be right?