Helmholtz equation stated that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\nabla^2 u(r,\theta,\phi) =-ku(r,\theta,\phi) = f(r,\theta,\phi) [/tex]

This is being used for Poisson equation with zero boundary:

[tex]\nabla^2 u(r,\theta,\phi) = f(r,\theta,\phi) [/tex]

and

[tex]u(a,\theta,\phi)=0[/tex]

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

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

If [itex]u(r,\theta,\phi)[/itex] is a constant number only, that cannot be right?

Please explain. Thanks

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# Question on using solution from Helmholtz equation in Poisson equation

Can you offer guidance or do you also need help?

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