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We discuss an investigation of student difficulties with the corrections tothe energy spectrum of the hydrogen atom for the intermediate field Zeemaneffect using the degenerate perturbation theory. The investigation was carriedout in advanced quantum mechanics courses by administering free-response andmultiple-choice questions and conducting individual interviews with students.We find that students share many common difficulties related to relevantphysics concepts. In particular, students often struggled with mathematicalsense-making in this context of quantum mechanics which requires interpretationof the implications of degeneracy in the unperturbed energy spectrum and howthe Zeeman perturbation will impact the splitting of the energy levels. Wediscuss how the common difficulties often arise from the fact that applyinglinear algebra concepts correctly in this context with degeneracy in the energyspectrum is challenging for students.

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