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

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• November 21st 2013, 11:15 AM
Alan0354
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?

Please explain. Thanks
• December 2nd 2013, 06:20 AM
Rebesques
Re: Question of using solution of Helmholtz equation to solve Poisson equation
Maybe your question would be answered easily, if you wrote

"...Poisson equation with zero boundary

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

etc"