# Thread: Question of using solution of Helmholtz equation to solve Poisson equation

1. ## Question of using solution of Helmholtz equation to solve Poisson equation

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?

$\nabla^2 w=f, w(a,\theta,\phi)=0$