Tutorials on thinking about quantum entities

developed by Benjamin W. Dreyfus, Jessica R. Hoehn, Erin Ronayne Sohr, Noah D. Finkelstein, Ayush Gupta, Andrew Elby, Kathleen Hinko

This page contains tutorials designed to support thinking about quantum entities and tutorials designed to support various kinds of reasoning with mathematical representations.

In most cases these tutorials are not designed to introduce new content, but can be used alongside other course materials and can help students be more reflective about the physics content.

Each tutorial is intended for an approximately 1-hour session. They are intended to be done in groups of 3-5 students discussing the questions in a group, with a facilitator circling among the groups.

They are not intended for the answers to be written up and handed in, and in many cases there is not a single correct answer, but instructors might decide to give follow-up questions on homework and exams that build on the tutorial questions.

Quantum Entities:

The tutorials on thinking about quantum entities were developed to support students in transforming their ontological conceptions about quantum phenomena: their sense of whether something is a particle, a wave, or some other kind of thing. In addition, the tutorials are intended to support students’ metacognitive awareness of their own ontological conceptions: thinking about their own thinking, and deciding which ontologies to use when.

The tutorials were first designed to be used in a modern physics course for engineering students; however, we have also found that they have sparked fruitful discussions among physics majors.

Mathematical Sensemaking (MSM):

The set of tutorials on mathematical sensemaking were developed to support students in making various kinds of connections between mathematical representations and physical scenarios.

The Doppler Cooling and Stern-Gerlach tutorials have students build mathematical representations from refined intuitions around experimental set-ups and results. The Doppler Cooling tutorial is designed for use in introductory or intermediate quantum courses and the Stern-Gerlach is geared towards upper-level courses.

These tutorials were designed in partnership with many undergraduate students at the University of Maryland, including: Vibhor Goel, Daelijuck Shin, Kun Do, and Rohan Rajagopalan.

The Infinite Square Wells tutorials guides students in fluidly moving through different forms of reasoning (e.g. with physics principles or mathematical formalism) to make sense of different kinds of objects, such as mathematical equations or physical concepts. These forms of reasoning more specifically include using math to understand physics, using physical principles to reason about math, using math to reason about math, and using physics concepts to reason about physics.  

These materials are open-source; anyone is welcome to access and adapt them. Reviewing instructor guides might guide adaptation as they reveal the intent and some of the results we have observed with students. We ask for contact information so that we can follow-up with people who are using the materials. If you wish to not provide contact information, leave the form blank.

If you are interested in implementing or adapting any of these tutorials for your course, or if you have any questions, please contact Ayush Gupta at ayush@umd.edu.

Quantum Entities Tutorial 1: Waves, Photons, and Energy

Quantum Entities Tutorial 2: Where was the photon?

Quantum Entities Tutorial 3: Plane waves and wave packets

Quantum Entities Tutorial 4: Particle in a box

Quantum Entities Tutorial 5: Tunneling

Quantum Entities Tutorial 6: Electron in a wire

Quantum Entities Tutorial 7: Energy and position

Quantum Entities Tutorial 8: Doppler cooling

Quantum Entities Tutorial 9: Zeeman effect

Quantum Entities Tutorial 10: LEDs

ZIP files

  • Download the Complete set of pdf tutorials:
  • Download the Complete set of doc tutorials:
  • Download the Complete set of pdf instructor guides:
  • Download the Complete set of doc instructor guides:

MSM Tutorial 1: Stern Gerlach Experiment

  • Download the Stern Gerlach Printable Links: Stern Gerlach Printable Links.pdf
    Links contained in the Stern Gerlach Tutorial
  • Download the Stern Gerlach Instructor Guide:
  • Download the Stern Gerlach Tutorial:
    Parts I and II

MSM Tutorial 2: Doppler Cooling

  • Download the Doppler Tutorial Parts 1 and 2:  or  Doppler Cooling Tutorial Parts 1 and 2.docx
    Doc or PDF file
  • Download the Doppler Tutorial Parts 1 and 2 Instructor Guide: Doppler Cooling Instructor Guide.pdf

MSM Tutorial 3: Infinite Square Wells


This work is supported by NSF-DUE 13-22734, 13-23129, 16-25797, and 16-25824.