Using network analysis techniques to probe student connections between Dirac notation and wave function expressions

Author / Creator

PERC SM21 (2021)

Conferences

PERC SM21 Poster Session 2C (2021)

Available as

Online

Summary

As part of an effort to examine student understanding of mathematical representations in quantum mechanics (QM), online survey tasks were designed and administered to students at the end of their u...

As part of an effort to examine student understanding of mathematical representations in quantum mechanics (QM), online survey tasks were designed and administered to students at the end of their upper-division QM courses at multiple institutions. Tasks were designed to find expressions and concepts that were related or viewed as similar in students' minds, and to determine what concepts and properties were ascribed to various expressions. Network analysis techniques were used to identify conceptual connections between expressions within and between Dirac, wave function, and standard vector notations. Community detection algorithms were used to study similarity between expressions, and network distance algorithms were used to study similarity between quantum mechanical concepts. Connections were found between Dirac expressions and vector expressions. Also, distinct single- and multiple-term communities were identified. Network analysis confirmed some clear conceptual connections, including between unit vectors and basis vectors, probability and probability amplitude, and eigenvectors and basis vectors.

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