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.

Highlights

  • Learning quantum mechanics (QM) is challenging even for advanced undergraduate and graduate students [1,2,3,4]

  • Investigations of student difficulties in QM are important for developing curricula and pedagogies that help students develop a solid grasp of QM [5,6,7,8]

  • No prior research studies have focused on student difficulties with the representations of quantum operators corresponding to observables in the context of Dirac notation, a compact and convenient notation commonly used in advanced QM

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Summary

Introduction

Learning quantum mechanics (QM) is challenging even for advanced undergraduate and graduate students [1,2,3,4]. No prior research studies have focused on student difficulties with the representations of quantum operators corresponding to observables in the context of Dirac notation, a compact and convenient notation commonly used in advanced QM. We discuss an investigation of student difficulties with representations of quantum operators corresponding to observables acting on quantum states in the position and momentum representations when using Dirac notation. One goal of many advanced QM courses is to help students learn how to represent a concept in different representations and use a representation that makes the problem solving task easier in a given context. The same position eigenstate, in the momentum representation, can be represented as DN Position operator xacting on position eigenstate

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