“What makes it eigen-esque-ish?”: A form-function analysis of the development of eigentheory concepts in a quantum mechanics course

Authors

Megan Wawro, Virginia Tech
Kaitlyn Stephens Serbin, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

6-2025

Abstract

Eigentheory concepts are central in mathematics and physics; they serve multiple functions, such as symbolizing physical phenomena and facilitating mathematical computations. Words and meanings associated with eigentheory develop and vary over time, as do their associated symbols. In this study, we investigate how “eigen” develops over time in one quantum mechanics course by analyzing form-function relations (Saxe, 1999) for eigentheory concepts over 22 class sessions. We share results concerning our microgenetic and ontogenetic analyses of the creation of form-function relations and their shifts over time by characterizing the continuity and discontinuity of the various functions and forms associated with concepts such as eigenequation, eigenstate, and eigenvalue. We illustrate how the use of prior functions with new forms contributed to the class community’s common ground for the use of eigentheory concepts in quantum mechanics, from familiar mathematical settings to the applicability of those concepts in the specific quantum mechanical contexts of spin, energy, and position.

Comments

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

Recommended Citation

Wawro, Megan, and Kaitlyn Stephens Serbin. "“What makes it eigen-esque-ish?”: A form-function analysis of the development of eigentheory concepts in a quantum mechanics course." Educational Studies in Mathematics (2025): 1-24.
https://doi.org/10.1007/s10649-025-10390-4

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Educational Studies in Mathematics

DOI

10.1007/s10649-025-10390-4