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Eigenvalue problem

  1. May 2, 2010 #1
    [URGENT] Eigenvalue problem

    1. The problem statement, all variables and given/known data
    [PLAIN]http://img228.imageshack.us/img228/4990/111em.png [Broken]


    2. Relevant equations
    Sturm-Liouville equation?


    3. The attempt at a solution
    I guess I'm just totally lost here. I've no idea how to start. It seems to me that maybe solving for solutions directly is ok, but that's near impossible in this case. I think there's some clever way around.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 2, 2010 #2

    vela

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    Re: [URGENT] Eigenvalue problem

    Plug f(x) into the eigenvalue equation and use the Laplacian in spherical coordinates in n dimensions to expand the lefthand side.
     
  4. May 2, 2010 #3
    Re: [URGENT] Eigenvalue problem

    Thanks!

    How about g(x)? How do I prove g(x) is also a solution?
     
  5. May 2, 2010 #4

    vela

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    Re: [URGENT] Eigenvalue problem

    Same way, I'd imagine.
     
  6. May 2, 2010 #5
    Re: [URGENT] Eigenvalue problem

    Well, I tried to do the same thing, but I just can't reach the same conclusion. Where does k come from? How do I get that term with k?

    Thanks,
     
  7. May 2, 2010 #6

    vela

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    Re: [URGENT] Eigenvalue problem

    It should come from the Laplacian acting on the spherical harmonic.
     
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