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Exploring student ideas on change of basis in quantum mechanics

Giaco Corsiglia1, Benjamin P. Schermerhorn2,3, Homeyra Sadaghiani3, Armando Villaseñor3, Steven Pollock1, and Gina Passante2

  • 1Department of Physics, University of Colorado, Boulder, Boulder, Colorado 80309, USA
  • 2Department of Physics, California State University, Fullerton, Fullerton, California 92831, USA
  • 3Department of Physics and Astronomy, California Polytechnic University Pomona, Pomona, California 91768, USA

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Phys. Rev. Phys. Educ. Res. 18, 010144 – Published 6 June, 2022

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.18.010144

Abstract

A common task when problem solving in quantum mechanics, including in a spins-first curriculum, involves changing the basis of a given state. Our research in undergraduate quantum mechanics courses at three institutions explores student thinking about basis, basis expansion coefficients, and change of basis in the context of spin-½ systems. Our investigation is based on conceptual and computational written questions as well as student reasoning interviews. We identify student ideas about whether and how changing basis affects the state, examine how students perceive notation as indicative of choice of basis, explore students’ interpretations of the structure and meaning of a basis expansion, and identify the range of methods students employ when changing basis. For instance, we find a recurring idea that changing basis alters the physical system, and observe that some students chose to relabel the ket representing a quantum state vector after changing basis. Together, these results paint a broad, qualitative picture of a variety of ways that students grapple with basis and change of basis, with potential implications for instruction.

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Phys. Rev. Phys. Educ. Res. 18, 010144– Published 6 June, 2022
  • Received 16 November 2021
  • Accepted 7 April 2022
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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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