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arXiv:1510.01299 · Physics Education Research Conference (PERC)

Investigating Student Difficulties with Time dependence of Expectation Values in Quantum Mechanics

Emily Marshman, Chandralekha Singh

Published Feb 1, 2014• 15 citations

Abstract

Quantum mechanics is challenging even for advanced undergraduate and graduate students.In the Schrödinger representation, the wave function evolves in time according to the time dependent Schrödinger equation.The time dependence of the wave function gives rise to time dependence of the expectation value of observables.We have been exploring the difficulties that advanced undergraduate and graduate students have with time dependence of expectation values in quantum mechanics.We have developed and administered conceptual free response and multiplechoice questions to students to investigate these difficulties.We also interviewed 23 students individually using a thinkaloud protocol to obtain a better understanding of the rationale behind students' written responses.We find that many students struggle with time dependence of expectation values of observables.We discuss some findings.

DOI: 10.1119/perc.2013.pr.049

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Quantum mechanics is challenging even for advanced undergraduate and graduate students.In the Schrödinger representation, the wave function evolves in time according to the time dependent Schrödinger equation.The time dependence of the wave function gives rise to time dependence of the expectation value of observables.We have been exploring the difficulties that advanced undergraduate and graduate students have with time dependence of expectation values in quantum mechanics.We have developed and administered conceptual free response and multiplechoice questions to students to investigate these difficulties.We also interviewed 23 students individually using a thinkaloud protocol to obtain a better understanding of the rationale behind students' written responses.We find that many students struggle with time dependence of expectation values of observables.We discuss some findings.

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. I.

Dirac notation is often used in upper level quantum mechanics courses, but students struggle with this representation.To investigate the difficulties that advanced students (i.e., upper-level undergraduate and graduate students) have while translating state vectors in Dirac notation to wave functions in position and momentum representations, we administered free-response and multiple-choice questions and conducted individual interviews with students.We find that students display common difficulties with these topics.

We investigate the difficulties of advanced undergraduate students toward the end of a full year upper-level quantum mechanics course with concepts related to quantum measurements and time development. Our analysis is based upon a test administered to 89 students from six universities and interviews with 9 students. Strikingly, most students shared the same difficulties despite variations in background, teaching styles, and textbooks. Concepts related to stationary states, eigenstates, and time dependence of expectation values were found to be particularly difficult. An analysis of written tests and interviews suggests that widespread misconceptions originate from an inability to discriminate between related concepts and a tendency to overgeneralize.