Abstract
As part of an effort to examine student understanding of mathematical representations in quantum mechanics, online survey tasks were designed and administered to students at the end of their upper-division QM courses at several institutions. Virtual task-based clinical interviews were also conducted in the following semester with students at the University of Maine. Tasks were designed to find expressions and concepts that were related or viewed as similar in students’ minds, and to determine what concepts were ascribed to various expressions. Geometric concepts, including vectors and dot products, were used to describe various expressions, as were physical concepts such as quantum states and probabilities of physical measurements. Multiple physical and mathematical concepts were often invoked for a single expression, and vice versa. Sherin’s symbolic forms framework was used to guide analysis, and potential symbolic forms used by students for expressions in both Dirac notation and wave function notation were identified.
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