  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".
