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.
Quantum mechanics is one of the crowning achievements of the human scientific enterprise. Yet only a small percentage of the general population has a detailed understanding of the principles of quantum mechanics. Why? Because it is hard? For sure, quantum mechanics requires us to understand phenomena that do not fit with our everyday experience, or even common sense. But, we should feel an obligation to help more people understand the bizarre quantum world. Not just because doing so helps the general population understand why science is important, and possibly even helps them understand why we need to fund science. But, because knowledge leads to empowerment. Everyone should know something about the quantum world. They should know the reality, not the science fiction, and most certainly not a "dumbed down" version that loses the true meaning. Sure this is a challenge, but it is possible. We should do this as best we can. We can start by making sure people know what Feynman actually meant when he said "no one understands quantum mechanics." He did not mean it was beyond human comprehension, he was describing the concept of indeterminacy, what he called the quantum mystery. While it does remain a mystery, understanding quantum mechanics principles need not be one. Let's work together to bring the quantum world to everyone. Scientists should not be the only ones to have all the fun!
Our work in this area has only just begun. Already our course Quantum Mechanics for Everyone, has already been seen by tens of thousands of students and it seems to work well in describing the concepts of superposition and entanglement using only high-school-level math. Read our report about this work in The Physics Teacher
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 1937, Dirac wrote a paper promoting using complex analysis in quantum instruction via the Laplace method. This is the original way Schrödinger solved the quantum problem for hydrogen in 1926. This method develops solutions for bound states and for continuum states as contour integrals over the complex plane. With a little experience, one can construct solutions for all problems that can be solved with confluent hypergeometric functions (solutions involving Legendre polynomials are not solvable this way). The benefit of doing this, aside from showing something different from the Frobenius approach, is to teach students how to both become comfortable with and to have experience with complex analysis. This training can then be used to learn more complicated topics, such as many-body Green's functions, or quantum field theory, more easily. To see how this works in practice, see our paper about how Schrödinger solved hydrogen.
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.
One of the interesting benefits of our on-line education courses is that we became connected with a community of scientifically talented, but not formally trained, individuals who are motivated to work on science. Many of these citizen scientists are at the level of undergraduate seniors and are ready for properly mentored researcher experiences. We have capitalized on involving this talented group of individuals to engage in scientific projects (mainly focused on quantm pedagogy) that is published in peer-reviewed journal articles. We call this process Deep Citizen Science. We find one can recruit numerous talented citizens from online MOOC courses. This approach can be duplicated in many fields where the research work involves theory or computation. We encourage others to learn how we do this and to follow in this pursuit themselves. For more details, look at our Citizen Science section of 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.