Does anybody know what the use of the Laguerre Differential Equation would be? I am having a hard time finding what areas of physics this diff. eq. is used in. Thanks.
It arises in solving Schrödinger's Equation to find the quantum-mechanical wave function of hydrogen. Specifically, it's associated with the radial part of the wave function. See this site, for example.
(Hmm, I see it doesn't mention Laguerre's equation specifically by name, but it does come up with the Laguerre polynomials which are part of the solution.)
Thank you, that site looks like it will help out quite a bit. It looks like it give a much more detail explanation that a lot of the other site I have seen.