PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Student meanings for eigenequations in mathematics and in quantum mechanics
Page: 638
Students encounter advanced mathematical concepts in both mathematics classes and physics classes. What meanings do they develop about the concepts across the various contexts? Our research project investigates students' meanings for eigentheory in quantum mechanics and how their language for eigentheory compares and contrasts across mathematics and quantum physics contexts. We present students' interpretations of a canonical mathematical 2x2 eigenequation, a spin-½ operator eigenequation, and a spin-½ operator equation in which the operation "flips" the spin state. In individual, semi-structured interviews, 9 quantum mechanics students were asked to explain what the first two equations meant to them and then to compare and contrast how they conceptualize eigentheory in the two contexts. They were then asked to discuss the third equation. Using discourse analysis, results characterize students' nuanced imagery for the equations and highlight instances of synergistic and potentially incompatible interpretations.