Exploring student preferences when calculating expectation values using a computational features framework

Abstract

Undergraduate quantum mechanics (QM) uses a variety of notations, each with their own advantages and constraints, for representing quantum states and carrying out individual calculations. An example of this can be seen when calculating expectation values, which can be solved using several different methods. Analysis of written exam data given at three universities (teaching spins-first QM) showed students were more likely to use matrix or integral calculation in situations where it is much simpler to use a summation method. By adapting the structural features framework by Gire and Price, we are able to answer questions regarding how and why students use different methods. We analyze student responses to expectation value problems administered in interviews conducted at two universities in the middle and end of the semester to highlight specific areas of difficulty and features of the methods which led to students' choices of one method over another.

Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics

“…Using problem-solving interviews with students as insight into how their reasoning interacts with these features, Gire and Price found that students in their study readily used Dirac notation, and that the structural features vary across the different notations as well as among several contexts within quantum mechanics. Building from this work, Schermerhorn et al [30] investigated students' selection of different representation methods for calculating expectation value problems in quantum mechanics, specifically with expectation values of spin-½ particles, energy, and position. Schermerhorn et al adapted Gire and Price's structural features framework to highlight the computational features present in students' work.…”

Applying a symbolic forms lens to probability expressions in upper-division quantum mechanics

“…Previous work has also looked at the affordances and limitations of the different notations used in QM [7,14,15]. Dreyfus et al posited a number of potential symbolic forms within Dirac notation that they suspect students likely develop through the course of an upper-division QM course [10], though little work has been done to address how students interpret and work with expressions across and within the different representations that are commonly used in upper-division QM.…”