Table of Contents

# Math Bits - Legendre's Equation

## Prerequisites

Students should be able to:

- Write a series as an infinite sum.
- Change the index on an infinite sum.
- Add infinite sums in sum notation.
- Write out the first few terms of an infinite sum.
- Identify that the coefficients of two infinite sums are independently equal if the infinite sums are equal.

## In-class Content

- Solving the $\theta$ equations using a Series Solution Method (Lecture, 90 minutes)

## Homework for Central Forces

- (SumShiftP)
- (RadialSeries)
*In this problem students solve the differential equation for the Laguerre Polynomials. The question is worded so that students see this as a practice problem on series solution methods rather than specifically the Laguerre equation which they can look up. By timing the assignment of this homework problem appropriately, it is possible to arrange to have the students complete this problem just before beginning the radial solution to the hydrogen atom; thus saving time in class solving the Laguerre equation.* - (Laguerre)

## Homework for Legendre Series

- (Legendre's Equation)
(Optional if not done in class)

- (LegendrePoly)
- (LaplaceSeparate)