PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Investigating Student Understanding of Eigentheory in Quantum Mechanics
Page: 2-457
An initial investigation into students’ understanding of Eigentheory using semi-structured interviews was conducted with students at the end of a first-semester course in quantum mechanics. Many physics faculty would expect students to have mastery of basic matrix multiplication after a course in Linear Algebra, and especially so after fairly extensive use of matrices in quantum mechanics in the context of Ising model spin problems. Using a previously published interview protocol by Henderson et al, student reasoning patterns were investigated to probe to what extent there reasoning patterns were similar to those identified among Linear Algebra students. Reasoning patterns appeared quite consistent with previous work; that is, students used superficial algebraic cancellation, and demonstrated difficulty interpreting their result even when they arrived at a correct solution. The interview protocol was modified slightly to probe whether or not students felt the tasks they were engaging in were mathematical or physics-related. Additional questions were added at the end of the protocol about how these concepts were used in their quantum mechanics course. Students were somewhat successful relating them to Hamiltonians and energy eigenvalues, but couldn’t articulate the type of physical situations where they might be useful.