How a representation-independent approach to quantum mechanics can aid student learning
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James K. Freericks 1 *
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1 Department of Physics, Georgetown University, Washington, DC, USA* Corresponding Author

Abstract

Quantum mechanics is traditionally taught in a specific representation—the position-space representation—because the time-independent Schrödinger equation is simplest to formulate there. But this leads to a number of conceptual issues both associated with language and with the formalism, especially if one starts more formally and then emphasizes representations for calculations. In this work, we describe a number of these issues and argue why restricting to a representation-independent formalism (that is, working with abstract operators and state vectors independent of any specific representation) fixes many of these issues. Then representations can be introduced later when needed for specific applications (but we find the need to do this can be sharply reduced from current paradigms).

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 22, Issue 8, August 2026, Article No: em2876

https://doi.org/10.29333/ejmste/18981

Publication date: 21 Jul 2026

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Article Downloads: 16

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