LASSP & AEP Seminar: John Thompson (Maine)
Student mathematical reasoning in undergraduate quantum mechanics: eigenvalue equations and probability expressions
The ability to relate physical concepts and phenomena to expressions in multiple mathematical representations is a crucial outcome of physics instruction, particularly in upper-division quantum mechanics (QM). Students work with various symbolic notations, some of which they may not have previously encountered. We have been investigating the ways that students in an upper-division, “spins-first” QM course reason about expressions commonly used in upper-division QM courses as well as how their ability to generate and interpret expressions is impacted by these multiple notations. One focus of research has been student interpretations of eigenequations, both in mathematics and quantum mechanics contexts, particularly for position as the observable quantity in the transition from discrete to continuous quantities. We have also explored student-generated probability expressions in Dirac and wave function notations, employing symbolic forms to analyze how participants interpret and reason about these expressions. Finally, in order to explore how students conceptualize expressions in Dirac and wavefunction notations in different instructional paradigms, a related study compared students’ conceptual connections between these expressions in spins-first and wave functions-first courses. Excerpts of these studies, their findings and implications for instruction will be discussed.
Bio: John Thompson is a professor in the Department of Physics at the University of Maine. His research interests include empirical investigations of (a) the interaction between student understanding of physics and the associated mathematics, and (b) student understanding of upper-division thermal physics (thermodynamics and statistical mechanics), both in physics and in engineering courses. He is PI on grant projects working with colleagues at UMaine and across the country conducting research and developing instructional resources in these areas.
John earned a B.S. in physics in 1990 from Rensselaer Polytechnic Institute, a master’s in physics from Brown University in 1992, and a Ph.D. in physics from Brown in 1998. His doctoral dissertation was in experimental surface physics.