Student difficulties with representations of quantum operators corresponding to observables

TL;DR

This study investigates the specific difficulties faced by upper-level physics students in understanding and representing quantum operators for observables using Dirac notation, through assessments and interviews.

Contribution

It identifies common student misconceptions and challenges with quantum operator representations, providing insights for improving quantum mechanics instruction.

Findings

Students struggle with Dirac notation for quantum operators.

Common misconceptions include misunderstandings of operator action and eigenstates.

Data highlights specific areas where instruction can be improved.

Abstract

Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found.