# Active Quantum Mechanics

### Tutorials and writing assignments for engaging students in the study of quantum mechanics.

[Overview] [Syllabus] [Tutorials] [Writing Assignments] [Credits] [Terms of Use] [Presentations]

## Overview

This page contains active-learning tutorials and writing assignments that I have developed for teaching upper-level undergraduate quantum mechanics. The tutorials focus on the mathematical formalism of quantum mechanics (I use Griffiths *Introduction to Quantum Mechanics* as the main text). Most of the tutorials were developed by converting the derivations and sample problems I used to lecture about into activities for my students to complete during class time. The writing assignments focus on the interpretation of quantum mechanics, and particularly the role of experiments in guiding our interpretation. [Note: my course is a designated “writing intensive”

course at Berry.]

I teach the course using interactive methods. Students work in small groups (usually 2) to complete worksheet-based tutorials during class time. Occasionally I lecture or demonstrate something using computer software. Students also do fairly typical homework problems, and complete their writing assignments, on their own.

## Syllabus and Projects

The syllabus for the course, which provides a list of topics as well as some details about how I run the course, is available below.

## Tutorials

The table below contains a list of tutorials, and some lecture notes (including Maxima CAS notebooks), on various topics that are typically covered in an upper-level undergraduate quantum mechanics course. The tutorials are designed to be used in a single 50 minute class period. You can download the PDF files for all of the tutorials and/or notes using the link below.

You are free to use (and even change) the worksheets, but please see the Terms of Use before doing so. If you wish to edit the worksheets, and you know how to use LaTeX (or are willing to learn), you can download a package containing all the .tex files and other necessary files (images, etc.) for all of the worksheets.

Here are the download links:

- PDF tutorials: ActiveQuantumTutorials
- PDF/Maxima Notes: ActiveQuantumNotes
- LaTeX source for tutorials: ActiveQuantumTex

Please watch out for typos and other errors in these handouts. I cannot guarantee that they are without flaws – but the handouts posted here are all materials that I have used in my own class. Please work carefully through the exercises yourself before you give them to your students! Finally, I apologize for the fact that some of the notes are just scanned copies of hand-written pages. I promise to convert these into LaTeX the next time I teach the course.

Tutorial/Notes | Griffiths Sections |
---|---|

Schrodinger Equation Notes, Math Tips | 1.1-1.2 |

Probability and Prediction | 1.3-1.4 |

Momentum and Uncertainty | 1.5-1.6 |

Energy Eigenvalue Problem Notes, Physicality Conditions | 2.1 |

Infinite Square Well | 2.2 |

Infinite Square Well Notes, ISW Classical/Quantum Notes | 2.2 |

Properties of Bound States | NA |

Harmonic Oscillator (Series Solution) | 2.3 |

Harmonic Oscillator (Commutators and Ladder Operators) |
2.3 |

Harmonic Oscillator (Algebraic Solution) | 2.3 |

Free Particle Notes | 2.4 |

Free Particle | 2.4 |

Delta Well | 2.5 |

Finite Square Well | 2.6 |

Finite Well Notes, Finite Well Maxima Notebook | 2.6 |

Scattering I: the Delta Well | 2.6 |

Scattering II: the Step | 2.6 |

Dirac Notation Notes | 3.1 |

Dirac Notation | 3.1 |

Observables and Operators | 3.2-3.3 |

Eigenstates of Hermitian Operators Notes, Useful Bases Notes | 3.3 |

Statistical Interpretation | 3.4 |

Generalized Uncertainty Principle | 3.5 |

Using Dirac Notation | 3.6 |

Spherical Harmonics Notes, SHPlotter Maxima Notebook | 4.1 |

Spherical Harmonics | 4.1 |

Hydrogen Atom Notes, Hydrogen Atom I | 4.2 |

Hydrogen Atom II | 4.2 |

Angular Momentum | 4.3 |

Spin Notes | 4.3-4.4 |

Spin | 4.4 |

Spin Matrices Maxima Notebook | 4.4 |

Electron in a Magnetic Field | 4.4 |

Addition of Angular Momentum | 4.4 |

Identical Particles | 5.1 |

Exchange Forces | 5.1 |

Perturbation Theory Notes | 6.1 |

Non-degenerate Perturbation Theory | 6.1 |

Change of Basis Notes, Degenerate Perturbation Theory | 6.2 |

Degenerate Perturbation Theory Maxima Notebook | 6.2 |

## Writing Assignments

**Long Paper:**This assignment focuses on the Stern-Gerlach experiment. The goal is to show students how the results of experiments force us into some of the strange ideas of quantum mechanics. Students conduct their own experiments using the SPINS program (originally created by Schroeder and Moore) and interpret the results. The package includes the writing prompt, a JAR file containing both the SPINS Java program as well as the curricular materials for conducting the required experiments, peer review instructions, and rewrite instructions.**Short Paper 1**: This assignment focuses on the double-slit experiment. Students respond to John Wheeler’s analysis of the double-slit experiment in his article “Law without law” (see below). This paper forces students to confront the “measurement problem” in quantum mechanics. The package contains the writing prompt and a grading rubric.**Short Paper 2**: This assignment focuses on an experimental verification of decoherence using thermal emission from buckyballs conducted by Anton Zeilinger and colleagues. Students are asked to analyze the experimental data to determine whether or not this experiment constitutes a clear demonstration of decoherence. They are then asked how decoherence applies to the behavior of macroscopic systems (like Schrodinger’s Cat). The package contains the writing prompt and a grading rubric.**Old Short Paper 2**: This assignment focuses on the EPR experiment. Students read an article by Alain Aspect on recent experimental verifications of the violation of Bell’s Inequality. The writing assignment forces students to address the possible conclusions that can be drawn in light of these experiments, and also to evaluate which of these conclusions is the most sensible (in their own view). [Note: I regretfully no longer use this assignment. I just can’t fit it in along with everything else. What is listed as Short Paper 2 above used to be Short Paper 3, back when I still used this assignment.]**Brief Essays**: This document lists a series of brief essay questions that are used to ensure that students keep up with their reading and think about what they have read. These questions deal with material from Lindley’s*Where does the weirdness go?*(see below).

## Resources

Resources for the writing assignments.

- David Lindley,
*Where does the weirdness go?*(Basic Books, 1996). - SPINS applet: available online. See also Schroeder and Moore, “A computer-simulated Stern-Gerlach laboratory,”
*American Journal of Physics***61**, 798-805 (1993). - John Wheeler, “Law without law,” in
*Quantum Theory and Measurement*ed. by Wheeler & Zurek (Princeton Univ. Press, 1983). - Alain Aspect, “Bell’s inequality test: more ideal than ever,”
*Nature***398**, 189-190 (1999). - Lucia Hackermuller, Klaus Hornberger, Bjorn Brezger, Anton Zeilinger, and Markus Arndt, “Decoherence by the emission of thermal radiation” available online.

## Terms of Use

All of the materials on this page are available free of charge. Feel free to download the materials and explore them with no obligation whatsoever. However, if you use any of these materials in a class please contact me (ttimberlake@berry.edu) to let me know. I would like to receive feedback on the tutorials (especially if you find an error!) and I would like to keep track of where they are being used. If you make any modifications of the tutorials I would like to know about it (if you made it better then I want to use your improved version!).

All

of the curricular materials listed on this page are copyrighted by Todd Timberlake and are licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License. You may modify and redistribute these materials for non-commercial use as long as you clearly cite the original author (Todd Timberlake) and release the materials under the same license.

## Presentations on this Material

The items below are from presentations I have given about my

quantum mechanics curricular materials.

- “Turning Quantum Mechanics Course Notes into Tutorials,” invited talk given at the
*2011 Summer Meeting of the American Association of Physics Teachers*, Omaha, NE, August 2011. Slides: ActiveQuantum - “Writing-Intensive Quantum Mechanics,” talk given at the
*2006 Winter Meeting of the American Association of Physics Teachers*, Anchorage, AL, January 2006. Slides: WIQuantum