1. (20 points) The Laguerre polynomial, Ln(x), are the solutions to the Laguerre differential

equation:

xy" + (1x)y' + ny=0 y'(0) = n!, n = 1, 2, 3...

(1)

Laguerre polynomials are essential in quantum mechanics as the are apart of the solution to the

Schrödinger equation for a one-electron atom, with many applications to physics and chemistry.

a. Of the methods presented in class, determine the appropriate method to use to solve the

Laguerre differential equation.

b. Find L3(2), in other words solve (1) with n = 3.