Improving Student Construction of a Quantum Mechanical Position Eigenvalue Equation: Preliminary Findings

Spins-first quantum mechanics (QM) courses are increasingly common due to multiple perceived affordances. Prior research in both physics and mathematics education has characterized student understanding of and reasoning about QM eigenvalue equations, particularly in spins-first courses. As part of an effort to examine and support students’ mathematical sensemaking in the transition from discrete to continuous systems in spins-first QM, students were asked to construct an eigenvalue equation for a one-dimensional, continuous position operator after approximately six weeks of instruction in the contexts of spins, but prior to any instruction in the context of positions. Few students constructed an equation of the correct form, and only a subset of those appropriately interpreted their equation. To address this, we are developing an instructional sequence (clicker question series and tutorial activity) to scaffold continuous position eigenvalue equation construction with explicit references to discrete spin eigenvalue equations. We discuss some aspects of the instructional materials development and implementation. While the sequence generally guided students to a correct equation and appropriate interpretation, there is evidence of room for improvement.