Numerical calculations (what many call computational physics) is a core tool in modern physics. With numerical methods it’s possible to solve problems that would otherwise be impossible. Most physics students and educators have at least some exposure to the wave equation. It shows up in many different contexts—light, quantum mechanics, and even a simple wave on a string. However, it can be difficult to come up with non-trivial solutions to the wave equation. This text goes through the techniques to create a numerical model of the wave equation starting from the very basics and using free and open source tools such as Python and Web VPython.

Table of Contents

1 Introduction to Numerical Calculations: A Mass on a Spring

2 Waves on a String and the Wave Equation

3 Modeling a Wave with Many Masses and Springs

4 Wave on a String with the Finite Difference Method

5 Special Case: Standing Waves on a String

6 The One Dimensional Wave Function

7 The Eigenvalue Problem

8 Time Evolution of the Wave Function

9 Wave Functions in Two Dimensions

About the Author

Rhett Allain is an Associate Professor of Physics at Southeastern Louisiana. Besides his role as a physics educator, he is also an active science communicator. In 2010, Allain began writing about fun and interesting physics topics on WIRED.com. These initial blog posts lead to other opportunities including becoming the science advisor for both MythBusters and CBS MacGyver. He maintains an active YouTube channel (Dot Physics) and also writes at medium.com. In his spare time, he likes to take things apart but he can’t always put them back together.