Teaching quantum mechanics without waves or matrices

In 1925, quantum mechanics was discovered by Heisenberg in the form of matrix mechanics, which was quickly superseded by Schrödinger’s wave mechanics in 1926. The former worked in an energy eigenspace representation, while the latter predominately in a position-space representation. There is a third way to formulate quantum mechanics in a representation-independent fashion, that I call operator mechanics. In this talk, I will describe how operator mechanics works and show how to teach quantum mechanics this way. I will emphasize the importance of learning goals, of teaching conceptual ideas before formalism, of emphasizing experiments, and of modernizing topics to the second quantum revolution. This strategy has been used both in classes taught at Georgetown (primarily to undergraduates) and at edX (primarily to lifelong learners). Mathematicians often emphasize the importance in deveoping materials in a representation-independent way, but quantum mechanics is an outlier here, where nearly all treatments focus on the position-space representation. One of the interesting consequences of this approach is that it lowers the mathematical preparation required---in fact, one needs only high-school level algebra, geometry and trigonometry. It requires no calculus! The work discussed in this talk is summarized in a forthcoming book called Quantum Mechanics Done Right from Springer-Nature. It will be published in an open access format, with the electronic version being freely available to all.