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Math Help - Question of using solution of Helmholtz equation to solve Poisson equation

  1. #1
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    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
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  2. #2
    Super Member Rebesques's Avatar
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    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"
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