Approaches for improving students’ understanding of quantum mechanics

A quite different approach from the one presented by the authors of “Improving Students’ Understanding of Quantum Mechanics” may be appropriate at least for some classes of students. It might be called the pragmatic approach, teaching students to deal with a wide variety of problems while minimizing philosophical discussion. I took this approach for several years while teaching a course for graduate engineers at Stanford. ¹ The resulting course was surprisingly orthogonal to the traditional quantum course. Solving the Schrödinger equation became a minimal part of the subject; rather, tight-binding expansions allowed the student to use simple algebra to obtain a meaningful understanding of atoms, molecules, and solids. Transition rates and shake-off excitations provided understanding of a wide variety of phenomena.

I took the defensible stance that all of quantum mechanics is the direct consequence of a single assertion, wave–particle duality. The uncertainty principle and the Pauli principle are consequences, not independent conjectures. Quantum theory does not tell us that there will be a particle of spin ½ with the mass and charge of an electron, but it indicates how such a particle will behave if there is one. When the consequences seem puzzling, it is fair to say that one is simply having difficulty with the starting assertion.