• Open Access

Mathematical sense-making in quantum mechanics: An initial peek

Benjamin W. Dreyfus, Andrew Elby, Ayush Gupta, and Erin Ronayne Sohr
Phys. Rev. Phys. Educ. Res. 13, 020141 – Published 28 December 2017
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Abstract

Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and “science studies” have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.

  • Received 24 June 2017

DOI:https://doi.org/10.1103/PhysRevPhysEducRes.13.020141

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Physics Education Research

Authors & Affiliations

Benjamin W. Dreyfus1,2,*, Andrew Elby3,4, Ayush Gupta3,5, and Erin Ronayne Sohr3

  • 1Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, USA
  • 2STEM Accelerator Program, George Mason University, Fairfax, Virginia 22030, USA
  • 3Department of Physics, University of Maryland, College Park, Maryland 20742, USA
  • 4Department of Teaching and Learning, Policy and Leadership, University of Maryland, College Park, Maryland 20742, USA
  • 5Keystone Program, A. J. Clark School of Engineering, University of Maryland, College Park, Maryland 20742, USA

  • *bdreyfu2@gmu.edu

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Issue

Vol. 13, Iss. 2 — July - December 2017

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