- #1

Andrew Deleonardis

- 5

- 0

##\sin\theta\frac{d}{d\theta}(\sin\theta\frac{d\Theta}{d\theta})+\Theta(l(l+1)\sin\theta-m^2)##

The solution for this equation is the following associated laguerre polynomial:

##P^m_l(\cos\theta)=(-1)^m(\sin\theta)^m\frac{d^m}{d\cos\theta^m}\bigg(\frac{1}{2^ll!}\frac{d^l}{d\cos\theta^l}(cos^2\theta-1)^l\bigg)##

This equation is involved in solving the schrodinger equation for the hydrogen atom.

Even though I already know the answer, I would like to know HOW to solve it