[en] Understanding when and how to make limiting case approximations and why they are valid in a particular situation is a hallmark of expertise in physics. Using limiting cases can simplify the problem-solving process significantly and they often provide a means to check that the results obtained are reasonable. We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the limiting cases of 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. Here we first discuss the common student difficulties related to these concepts. We then describe how the research on student difficulties was used as a guide to develop and evaluate a quantum interactive learning tutorial (QuILT) which strives to help students develop a functional understanding of the concepts necessary for finding the corrections to the energy spectrum of the hydrogen atom for the strong field and weak field Zeeman effects. The development of the QuILT and its evaluation in the undergraduate and PhD level courses are presented. (paper)