Network Analysis of Student Interpretations of Dirac Expressions Across Curricula

Abstract

One important outcome of physics instruction is for students to be capable of relating physical concepts to multiple mathematical representations. In quantum mechanics (QM), students are asked to work across multiple symbolic notations, including some not encountered in previous coursework. To investigate student understanding of the relationships between expressions used in these various notations and generic vector expressions, a survey was distributed to students in upper-division QM courses at multiple institutions. The courses surveyed included those structured both as “spins-first” and “wave functions-first.” Network analysis techniques were used to compare student understanding of common expressions used in these courses, in both Dirac notation and wave function notation. Preliminary analysis suggests that, in addition to more distinct morphological grouping, students in “spins-first” courses also appear to conceptualize Dirac expressions as more vector-like than those in “wave-functions first” courses, consistent with the instructional emphasis.