The way we teach quantum mechanics is over 70 years old. It is heavily influenced by the course given by Robert Oppenheimer at Berkeley, which became the basis for the (hugely popular and influential) Schiff (1949) and Bohm (1951) textbooks. It was also influenced heavily by the third edition (1947) of Paul Dirac's quantum mechanics textbook. Back then, quantum mechanics was an advanced graduate class, and students were well-versed in differential equations, so using a differential-equation based, coordinate-space approach made sense. Since then, the time at which quantum mechanics is introduced to students has moved to the second year modern physics class. We now typically teach it three times, essentially the same way each time, and in many cases the students still don't really understand it when they have finished seeing it. It is often said that the sign of insanity is repeating something more than once and expecting a different result. Is our teaching of quantum mechanics insane?

I believe some of the reasons why we have become complacent is due to a lack of options for how to teach quantum mechanics. Just look at any of the scores of recently written textbooks. They all have nearly identical content, and it is hard to differentiate between which is an undergraduate and which is a graduate text, without reading the preface. You know a field is stale when a simple reordering of topics (as in the spins first movement) is viewed as a revolutionary change. Are there other options? There are! In our work, we focus on two main areas. One is to work with the material in a representation-independent fashion, focusing on operators, which we colloquially call operator mechanics (to differentiate it from matrix mechanics and wave mechanics). This way of working with quantum material has its origin with Pauli's solution of hydrogen in 1925 and with the abstract approach of Dirac from that time as well. It became firmly developed by Schrödinger in 1940, with the invention of his factorization method. Working with this material allows us to solve all of the same problems that are normally covered (often many more can now be covered). The second is based on Schrödinger's original solution of the hydrogen atom, which employed the Laplace method to solve the differential equation via contour integrals in the complex plane. Teaching this material at the graduate level offers students the opportunity to learn how to use ideas from complex analysis in their physics problem solving (indeed, Dirac advocated for this approach in 1937). Both the development of operator sense and the ability to work with ideas from complex analysis helps students who move into many-body physics or field theory. We owe it to our students to rethink how we teach quantum mechanics. Come join us in developing these new ideas!

To see how these ideas are developed, browse through the website using the above tabs and visit the blog. You can briefly learn more about other projects by expanding the sections below. You are guaranteed to learn something new! You may even be influenced to make changes in how you teach the material.

In the United States, physics majors are often introduced to quantum mechanics in their sophomore year, within the context of a Modern Physics class. This class will cover special relativity, maybe general relativity, and quantum mechanics. Following the introductory course, most programs will have one or two semesters of follow-up classes at the Junior-Senior level. The vast majority of these classes teach the material by motivating it using a historical context and then either use a spins first approach or a Schrödinger equation first approach. Both approaches use wavefunctions in the coordinate-space basis throughout. Some questions I have asked are, why do we motivate the class with a historical approach when students do not know how to model the motivating experiments classically? Why do we focus on using a formal development that requires so much math instruction (typically for the Froebenius method and delta functions) when these techniques are usually not used later in research?

At Georgetown, we developed a course motivated by physics education research and by what researchers typically use when working on quantum mechanics problems. This leads to a focus on the conceptual ideas of quantum mechanics and to the use of operators more than wavefunctions. Such an approach naturally is a representation-independent approach (preferred by mathematicians) and also allows one to emphasize quantum experiments more, as opposed to experiments that motivated quantum mechanics in the first place. We feel it is important to modernize quantum instruction in this fashion and help build a quantum-enabled workforce. This class is well poised to prepare students for the quantum sensing pillar of quantum information science. I have given a talk on this topic at the Chesapeake Section of the AAPT in April, 2021. We have a series of uncergraduate courses on edX to prepare for future work in quantum sensing. Mathematical and Computational Physics and Quantum Mechanics.

In our group, we do not perform physics education research (although anyone who does engage in PER and wishes to collaborate, please contact us). Instead, what we do is develop alternative pedagogical materials to provide instructors with choices about what they teach. The current field of quantum education is stale and is in need of fresh new ideas. We hope our work will inspire others to think of novel approaches to these different problems. See our list of current publications on our research page.

We write posts regularly on quora, especially to correct answers that are wrong or misleading in quantum mechanics. Check out my profile.