Student difficulties with finding the corrections to the energy spectrum of the hydrogen atom for the strong and weak field Zeeman effects using degenerate perturbation theory

TL;DR

This paper investigates student difficulties in understanding energy spectrum corrections of the hydrogen atom under Zeeman effects using degenerate perturbation theory, based on assessments and interviews in advanced quantum mechanics courses.

Contribution

It identifies common student misconceptions and challenges, providing insights for developing targeted educational tools for quantum mechanics concepts.

Findings

Students struggle with applying degenerate perturbation theory to Zeeman effects.

Common misconceptions include misunderstanding energy level splitting and perturbation calculations.

Results inform the design of instructional strategies to improve conceptual understanding.

Abstract

We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the strong and weak field Zeeman effects using degenerate perturbation theory. This investigation was carried out in advanced quantum mechanics courses by administering written free-response and multiple-choice questions and conducting individual interviews with students. We discuss the common student difficulties related to these concepts which can be used as a guide for creating learning tools to help students develop a functional understanding of concepts involving the corrections to the energy spectrum due to the Zeeman effect.