Investigating students’ implementation of and preference for the methods of solving for expectation values in quantum mechanics

A common activity in undergraduate quantum mechanics involves calculating expectation values. Analysis of written exam data given at three universities, using a spins-first curriculum, showed students had a tendency to use matrix or integral calculation in situations where it is simpler to use the summation method. To investigate students’ use of and preferences for the various methods, interviews were conducted at two of the universities in the middle and end of the semester. Adapting Gire and Price’s framework for categorizing structural features of different quantum mechanical notation, we analyze student responses to expectation value problems to highlight specific areas of difficulty and features of the methods which led to students’ choices of one method over another.