The Laguerre Differential Equation and Laguerre Polynomials

We consider the Laguerre Differential Equation which arises when seperating variables in the Schrodinger Equation for the hydrogen atom. The fact that the Laguerre equation admits polynomial solutions allow for radial solutions which have finite second moment. We study these polynomials solutions and assemble a collection of properties of these polynomials which will help us understand the solutions to the Schrodinger equation.
#mikethemathematician, #mikedabkowski, #profdabkowski