Speaker
Description
Quantum Mechanics is the upper-level undergraduate course that is often the most challenging in the core curriculum for physics majors. While most courses follow the more traditional track of starting with Schrödinger’s Equation and wave functions in position space, a recent trend favors an alternate approach that instead exposes students to simple spin-½ systems at the beginning. In the conventional curriculum, students often get mired in calculus and differential equations, which obscures the important and elegant fundamentals of QM. Many of the basic concepts (eigenvectors, operators, measurement) are firmly anchored not in calculus, but in linear algebra, including vector spaces, basis sets, etc. The spins-first approach gives students extensive experience with the mechanics of QM in the forms of Dirac and matrix notation, allowing them to focus on these new features and confront the physics that runs counter to classical mechanics.
After teaching QM for the first time in the Fall 2025 semester using the conventional method, we opted to “take the plunge” and embrace the spins-first approach in the current Fall 2026 semester. We have also added a low-stakes supplemental session that addresses the linear algebra alongside the quantum concepts discussed in class, enabling an open discussion forum and strengthening the students’ facility with the abstract math needed for QM. Thus far, we find that the students are motivated by the spins-first approach and readily engage in the supplemental sessions, appreciating the chance for discussions and clarifications of the linear algebra concepts with which they sometimes struggle. These sessions also leave time for the broader elements of QM, such as its interesting history, double-slit interference, entanglement, and proposed explanations of the measurement problem. In this talk, the background for this course focused on spins first will be presented, and some evidence for the validity of this approach will be provided.
