Allain R. Modeling Waves with Numerical Calculations Using Python 2025

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Allain R. Modeling Waves with Numerical Calculations Using Python 2025

Textbook in PDF format 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. I’m not going to expect that you have any previous knowledge about programming in python (or any other language). Python has a fairly simple syntax, but it can also be quite powerful. In this case we can use an online version of python called Web VPython. This means that a user won’t have to install anything to get this to function. Web VPython also has some other very useful features: Built in mathematical functions as well as vector operations. Simple methods for graphing (including animated graphs). Tools to build 3D visualizations for the motions of objects. Introduction to Numerical Calculations: A Mass on a Spring Waves on a String and the Wave Equation Modeling a Wave with Many Masses and Springs Wave on a String with the Finite Difference Method Special Case: Standing Waves on a String The One Dimensional Wave Function The Eigenvalue Problem Time Evolution of the Wave Function Wave Functions in Two Dimensions