How to teach quantum mechanics without matrices or waves

Speaker: Dr. Jim Freeicks
Affiliation: Georgetown University
Date: September 10, 2026

Abstract:

I will describe how to teach quantum mechanics without an emphasis on matrices or wavefunctions but instead teach it in a representation-independent fashion. This "operator mechanics" makes the material more accessible and allows us to introduce more experimental ideas into the classroom. Quantum pedagogy has been stuck in the differential equation paradigm developed just after World War Two, in spite of there being significant new advances since then. By placing operators in the forefront, many aspects of instruction simplify. For example, all calculations can be performed by using four fundamental operator identities (Leibniz product rule, Hadamard lemma, Baker-Campbell-Hausdorff formula, and the exponential disentangling identity). By teaching conceptual ideas first, students are able to reason about quantum phenomena before developing formalism. By reducing the math prerequisites, more students are able to study quantum mechanics, and more time can be devoted to the physics instead of teaching new mathematics. I will summarize a course taught at Georgetown in this fashion and will present some examples for how instruction changes in this new approach. These ideas have been collected in a new book, entitled "Quantum Mechanics Done Right: The shortest path from novice to researcher," which is now available from Springer as an open access book. If time is available, I will mention some ideas from our newest project to introduce quantum mechanics at the sophomore level by building from the classical physics they already know.