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Solution of the radial part of the laplace-equation

  1. Nov 29, 2012 #1
    1. The problem statement, all variables and given/known data
    I got the the radial part of the Laplace-Equation:

    [itex]r^2(\frac{d^2}{dr^2}U(r))=l(l+1)U(r)[/itex]

    Now I should show that the following solves the equation:

    [itex]a_l*r^l+\frac{b_l}{r^l}[/itex]

    3. The attempt at a solution
    29.11.1222-05-30rfq7k.jpg
    The problem is that I got l(l-1) instead of l(l+1) :(
     
  2. jcsd
  3. Nov 29, 2012 #2

    TSny

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    Gold Member

    Hello, and welcome to PF!
    The expression on the left is incorrect. See here for Laplace's equation in spherical coordinates.
     
  4. Dec 14, 2012 #3
    Sorry for the late answer. the ansatz was wrong, instead of [itex]a_r*r^l+\frac{b_l}{r^l}[/itex] it has to be:

    [itex]a_r*r^l+\frac{b_l}{r^{l+1}}[/itex]
     
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