Student difficulties with determining expectation values in quantum mechanics

TL;DR

This study investigates the conceptual and procedural difficulties faced by upper-level physics students in calculating expectation values in quantum mechanics, highlighting specific challenges with Dirac notation through various assessments.

Contribution

It provides detailed analysis of student misconceptions and difficulties in understanding and computing expectation values in quantum mechanics, especially using Dirac notation.

Findings

Students struggle with conceptual understanding of expectation values.

Procedural errors are common when applying Dirac notation.

Interviews reveal specific misconceptions about quantum observables.

Abstract

The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value of physical observables, especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students. Here, we discuss the analysis of data on student difficulties when determining the expectation value.