Solution of the radial part of the laplace-equation

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  • #1
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Homework Statement


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]

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) :(
 

Answers and Replies

  • #2
TSny
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Hello, and welcome to PF!

Homework Statement


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]

The expression on the left is incorrect. See here for Laplace's equation in spherical coordinates.
 
  • #3
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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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