RUME 25
2023
Omaha, Nebraska
Student Understanding of Eigenvalue Equations in Quantum Mechanics: Symbolic Forms Analysis
Page: 90
As part of an effort to examine students’ mathematical sensemaking (MSM) in a spins-first quantum mechanics (QM) course, students were asked to construct an eigenvalue equation (EE) for a one-dimensional position operator. Sherin’s symbolic forms were used in analysis. The data suggest three symbolic forms for an EE, all sharing a single symbol template but with unique conceptual schemata: a transformation which reproduces the original, an operation taking a measurement of state, and a statement about the potential results of measurement. These findings corroborate prior literature on a construction task rather than a comparison or deconstruction task, and with a continuous variable after instruction on discrete variables.