Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place. Commercial Alternative to JupyterHub.

Introduction

This is a work in progress and more activities will be added in the future. Check back later for a more tutorials

Please feel free to copy these documents and modify them according to your needs. I encourage you to make use of these in your classes.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Organization of This Document

This document contains a series of links to interactive SageMath worksheets. Each worksheet shows how to use various features of SageMath to teach quantum mechanics. The quantum mechanics topics are in the order they would be encountered in a traditional quantum mechanics course and show how to solve problems related to each topics. Additionally, each worksheet has a list of projects for students to further their understanding of quantum mechanics.

Introduction to SageMath

You can find numerous tutorials online for getting started with SageMath but here are a few of the better ones I've found.

• Try an interactive tutorial here

• Sage for Undergraduates is a textbook written by Dr. Gregory Bard. Free pdf versions of the text can be found here.

• A tutorial from San Diego State University

• Official SageMath tutorials

Editing SageMath Worksheets

You are encouraged to edit these worksheets for your students. This material is released under the CC-BY 4.0 license. Please modify these documents to fit the needs of your class and share your changes with others. Many of the earlier sections could be used in a Modern Physics course with a little editing.

Editing Tips

• Everything written in cells that start with %md on the first line are treated as Markdown cells using (%todo:find link to markdown)

• Starting a cell with %html treats everything in the cell as HTML code

• Double-click on the text of a cell to show the code

• The hashtag '#' is used in calculation cells to indicate comments that are not parsed by SageMath

See the ReadMe for directions on how to copy these documents into your SageMathCloud project

Quantum Mechanics Topics

- Wave Function of a Free Particle

[Free Particle Wave Function Interactive Worksheet](Free Particle Wave Function.sagews)

This worksheet covers the following SageMath features:

• Defining functions and variables

• Taking derivatives of a function

• Plotting functions

• Creating an animated plot

• Extract solution from a list of answers

• Solving algebraic equations

- 1D Particle in a Box

[Particle in a 1D Box Interactive Worksheet](Particle in a 1D Box.sagews)

This worksheet covers the following SageMath features:

• Solving differential equations

• Integrating a function

• Plotting functions

• Creating an animated plot

• Approximate numerical results

• Expand symbolic expressions

- Quantum Harmonic Oscillator

[Quantum Harmonic Oscillator Wave Function Worksheet](Quantum Harmonic Oscillator.md)

This worksheet assume you can integrate, differentiate, and plot simple graphs. The worksheet covers the following features:

• Solving differential equations

• Plot dotted, dashed, or solid lines

• Placement of plot titles

• Adding arrows and text to plots

• Simplify symbolic expressions

- Scattering and Tunneling from Step Potentials

[Scattering and Tunneling Worksheet](Scattering and Tunneling.sagews)

The worksheet covers the following features:

• Solving systems of equations

• Simplifying symbolic expressions

Future Worksheets

- Angular Momentum

- Hydrogen Atom

[](Need del in different coord systems for this) [](Take a look at Sympy libraries)

- Quantum Mechanical Matrix Operators in SageMath

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.