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Student understandings of discrete and continuous in quantum mechanics: A thematic analysis

Christian D. Solorio, Elizabeth Gire, and David Roundy

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Phys. Rev. Phys. Educ. Res. 21, 020158 – Published 16 December, 2025

DOI: https://doi.org/10.1103/4q6g-yq88

Abstract

Students in a spins-first quantum mechanics course often have difficulties transitioning from spin systems to continuous systems like the infinite square well. Our study investigates how students understand discrete and continuous quantities in quantum mechanics and the connections the students make between them. We interviewed six students who were concurrently enrolled in a junior-level spins-first quantum mechanics course with a computational lab. During the interview, students organized a set of 20 cards containing various quantum mechanics concepts and representations, including snippets of python code. Using a phenomenographic approach, we generated four themes: understandings of discrete, understandings of continuous, discreteness of representations, and discrete approximations of integrals. Participants often related discrete and continuous quantities in the context of code, suggesting that computational activities can support students in transitioning from discrete systems to continuous ones.

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Outline

Information

Phys. Rev. Phys. Educ. Res. 21, 020158– Published 16 December, 2025
  • Received 25 September 2023
  • Revised 29 July 2025
  • Accepted 4 November 2025
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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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