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Student understanding of eigenvalue equations in quantum mechanics: Symbolic blending and sensemaking analysis

A. R. Piña1,*, Zeynep Topdemir2, and John R. Thompson1,3

  • *anthony.pina@maine.edu, they/them/theirs
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Phys. Rev. Phys. Educ. Res. 20, 010153 – Published 18 June, 2024

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.20.010153

Abstract

As part of an effort to examine students’ mathematical sensemaking (MSM) in a spins-first quantum mechanics course during the transition from discrete (spin) to continuous (position) systems, students were asked to construct an eigenvalue equation for a one-dimensional position operator. A subset of responses took the general form of an eigenvalue equation written in Dirac notation. Symbolic blending, a combination of symbolic forms and conceptual blending, as well as a categorical framework for MSM, were used in the analysis. The data suggest two different symbolic forms for an eigenvalue equation that share a symbol template but have distinct conceptual schemata: A transformation that reproduces the original and to operate is to act. These symbolic forms, when blended with two sets of contextual knowledge, form the basis of three different interpretations of eigenvalue equations modeled here as conceptual blends. The analysis in this study serves as a novel example of, and preliminary evidence for, student engagement in sensemaking activities in the transition from discrete to continuous systems in a spins-first quantum mechanics course.

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Phys. Rev. Phys. Educ. Res. 20, 010153– Published 18 June, 2024
  • Received 5 March 2024
  • Accepted 13 May 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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