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

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.