RadialEquation 2006-01-15 14:25:11 2006-01-15 14:25:11 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here The radial equation is $$ - \frac{\hbar^2}{2m} \frac{d^2u}{dr^2} + \left [ V + \frac{\hbar^2}{2m}\frac{l(l + 1)}{r^2} \right ]u = Eu $$ It's derivation is straight forward using separation of variables with the Schr\"odinger equation in spherical coordinates.