Talk:PlanetPhysics/Radial Equation

Original TeX Content from PlanetPhysics Archive

%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: radial equation %%% Primary Category Code: 03.65.-w %%% Filename: RadialEquation.tex %%% Version: 2 %%% Owner: bloftin %%% Author(s): bloftin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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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 \htmladdnormallink{separation of variables}{http://planetphysics.us/encyclopedia/SeparationOfVariables.html} with the \htmladdnormallink{time independent Schr\"odinger equation in spherical coordinates}{http://planetphysics.us/encyclopedia/TimeIndependentSchrodingerEquationInSphericalCoordinates.html}.

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