Students' choices when solving expectation value problems

In quantum mechanics, one is often interested in the expectation value (or average) of different quantities. It is possible to find expectation values for many different physical systems, for example the energy or position of a particle in the infinite square well, the z-component of spin for an electron, or the angular momentum of an electron in a hydrogen atom. In addition to the different physical contexts where the expectation value can be calculated, there are several methods one can use to solve for the expectation value. Depending on the information given in the problem, it might be easiest to solve using an integral, matrix mathematics, or a finite summation. In this work we analyze student responses to expectation value exam questions in several different physical contexts from several institutions, with a goal of determining which calculation methods and representations students choose most frequently and if some methods are more likely to result in correct answers.