Student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect

TL;DR

This study investigates how advanced quantum mechanics students struggle with understanding and applying degenerate perturbation theory to the hydrogen atom's energy spectrum in the intermediate Zeeman effect, highlighting common conceptual and mathematical difficulties.

Contribution

It identifies specific student misconceptions and challenges in applying linear algebra and physical interpretation in degenerate perturbation theory within quantum mechanics.

Findings

Students struggle with mathematical sense-making in degeneracy contexts.

Common difficulties include interpreting the impact of the Zeeman perturbation.

Challenges arise from applying linear algebra concepts correctly with degeneracy.

Abstract

We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect using the degenerate perturbation theory. The investigation was 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 relevant physics concepts. In particular, students often struggled with mathematical sense-making in this context of quantum mechanics which requires interpretation of the implications of degeneracy in the unperturbed energy spectrum and how the Zeeman perturbation will impact the splitting of the energy levels. We discuss how the common difficulties often arise from the fact that applying linear algebra concepts correctly in this context with degeneracy in the energy spectrum is challenging for students.