Using Network Analysis Techniques to Probe Student Understanding of Expressions Across Notations in Quantum Mechanics
Published: 2022
Publication Name: Proceedings of the 24th annual conference on research in undergraduate mathematics education
Publication URL: http://sigmaa.maa.org/rume/RUME24.pdf
Abstract:
One important outcome of physics instruction is for students to be capable of relating physical concepts and phenomena to multiple mathematical representations. In quantum mechanics (QM), students are asked to work between multiple symbolic notations, some not previously encountered. To investigate student understanding of the relationships between expressions used in these various notations, many of which describe analogous physical concepts, a survey was distributed to students enrolled in upper-division QM courses at multiple institutions. Network analysis techniques were shown to be useful for gaining information about how students relate these expressions. Preliminary analysis suggests that students view Dirac bras and kets as more similar to generic vectors than to their physically analogous wave function counterparts, and that Dirac bras and kets serve as a bridge between vector and wave function expressions.
Riihiluoma, W., Topdemir, Z., & Thompson, J.R. (2022). Using network analysis techniques to probe student understanding of expressions across notations in quantum mechanics. In S. S. Karunakaran & A. Higgins (Eds.), Proceedings of the 24th annual conference on research in undergraduate mathematics education. The Special Interest Group of the Mathematical Association of America for Research in Undergraduate Mathematics Education. http://sigmaa.maa.org/rume/RUME24.pdf