Active Quantum Mechanics

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


Todd Timberlake
Associate Professor of Physics & Astronomy
Berry College
Mount Berry, GA

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


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.


The table below contains a list of tutorials, and some lecture notes, on various topics that are typically covered in an upper-level undergraduate quantum mechanics course. For each topic I provide a link for downloading the corresponding tutorial worksheet (in pdf format). The worksheets are designed to be used in a single 50 minute class period.

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. To download this package click the link below:

If you would like to edit the worksheets but need them in a different format please email me ( and I may be able to accommodate you.

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.

Topic Griffiths Sections Worksheet
Schrodinger Equation Notes 1.1-1.2 1SchrodingerEqution.pdf
Probability and Prediction 1.3-1.4 PredictingProbabilities.pdf
Momentum and Uncertainty 1.5-1.6 MomentumUncertainty.pdf
Energy Eigenvalue Problem Notes 2.1 2EnergyEigenvalueProblem.pdf
Infinite Square Well 2.2 InfiniteSquareWell.pdf
Infinite Square Well Notes 2.2 3InfinitSquareWellNotes.pdf
Properties of Bound States NA BoundStates.pdf
Harmonic Oscillator (Series Solution) 2.3 HOseries.pdf
Harmonic Oscillator (Commutators and Ladder Operators) 2.3 HOoperators.pdf
Harmonic Oscillator (Algebraic Solution) 2.3 HOalgebraic.pdf
Free Particle Notes 2.4 FreeParticleNotes.pdf
Free Particle 2.4 FreeParticle.pdf
Delta Well 2.5 DiracDelta.pdf
Finite Square Well 2.6 FiniteSquareWell.pdf
Finite Square Well Notes 2.6 4FiniteWellNotes.pdf
Finite Well Maxima Notebook (zipped)
Scattering I: the Delta Well 2.6 ScatteringI.pdf
Scattering II: the Step 2.6 ScatteringII.pdf
Dirac Notation Notes 3.1 DiracNotation.pdf
Dirac Notation 3.1 DiracNotation.pdf
Observables and Operators 3.2-3.3 Operators.pdf
Hermitian Operators Notes 3.3 5UsefulBases.pdf
Statistical Interpretation 3.4 Probabilities.pdf
Generalized Uncertainty Principle 3.5 GenUncertainty.pdf
Using Dirac Notation 3.6 UsingDiracNotation.pdf
Spherically Symmetric Potentials Notes 4.1 7SphericalHarmonics.pdf
Spherical Harmonics Maxima Notebook (zipped)
Spherical Harmonics 4.1 SphericalHarmonics.pdf
Hydrogen Atom I 4.2 Hydrogen.pdf
Hydrogen Atom II 4.2 Hydrogen2.pdf
Angular Momentum 4.3 AngularMomentum.pdf
Angular Momentum and Spin Notes 4.3-4.4 SpinNotes.pdf
Spin 4.4 Spin.pdf
Spin in Maxima 4.4 Spin Matrices Maxima Notebook (zipped)
Electron in a Magnetic Field 4.4 BFieldTutorial.pdf
Addition of Angular Momentum 4.4 AddingAngularMomentum.pdf
Identical Particles 5.1 IdenticalParticles.pdf
Exchange Forces 5.1 ExchangeForces.pdf
Perturbation Theory Notes 6.1 NDPTnotes.pdf
Non-degenerate Perturbation Theory 6.1 NDPT.pdf
Degenerate Perturbation Theory 6.2 DegPT.pdf
Degenerate Perturbation Theory in Maxima 6.2 Degenerate Perturbation Theory Maxima Notebook (zipped)

Writing Assignments


Resources for the writing assignments.

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 ( 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.


Todd K. Timberlake (