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Categorization of Quantum Mechanics Problems by Professors and Students

We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honors-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty members' categorizations were overall rated higher than those of students by three faculty members who evaluated all of the categorizations. The categories created by faculty members were more diverse compared to the categories they created for a set of introductory mechanics problems. Some faculty members noted that the categorization of introductory physics problems often involves identifying fundamental principles relevant for the problem, whereas in upper-level undergraduate quantum mechanics problems, it mainly involves identifying concepts and procedures required to solve the problem. Moreover, physics faculty members who evaluated others' categorizations expressed that the task was very challenging and they sometimes found another person's categorization to be better than their own. They also rated some concrete categories such as "hydrogen atom" or "simple harmonic oscillator" higher than other concrete categories such as "infinite square well" or "free particle".