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Question on using solution from Helmholtz equation in Poisson equation

  1. Nov 21, 2013 #1
    Helmholtz equation stated that
    [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
     
  2. jcsd
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