Investigating and addressing student difficulties with a good basis for finding perturbative corrections in the context of degenerate perturbation theory

作者：Christof Keebaugh, E. Marshman, C. Singh · 发表于：European journal of physics · 年份：2018 · DOI：10.1088/1361-6404/aac354 · 被引用次数：22 · 研究领域：Physics

Degenerate perturbation theory (DPT) is a powerful approximation method for finding the energies and the energy eigenstates for a system for which the time-independent Schrödinger equation is not exactly solvable and there is degeneracy in the unperturbed energy spectrum. However, many students struggle with DPT because they have difficulty identifying whether a given basis is a good basis for finding perturbative corrections and determining a good basis for a given system. Here, we first discuss an investigation of student difficulties with determining a good basis and finding the corrections to the energies and energy eigenstates in the context of DPT carried out in advanced quantum mechanics courses by administering free-response and multiple choice questions and conducting individual interviews with students. We find that students share many common difficulties related to this topic. We then describe how the research on student difficulties was used as a guide to develop and validate a quantum interactive learning tutorial (QuILT), which strives to help students develop a functional understanding of a good basis for finding the perturbative corrections in the context of DPT. We discuss the development and validation of the QuILT on DPT and its evaluation in undergraduate and graduate courses.