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Physics Education Research Conference (PERC)

Investigating student understanding of the stationary state wavefunction for a system of identical particles

Christof Keebaugh, Emily Marshman, Chandralekha Singh

Published Sep 1, 2020• 0 citations
Publisher

Abstract

We discuss an investigation of student difficulties with concepts related to the many-particle stationary state wavefunction for a system of non-interacting fermions or bosons in cases in which the many-particle stationary state wavefunction can be written as the product of the spatial and spin parts.The investigation was carried out in advanced quantum mechanics courses by administering free-response and multiple-choice questions and conducting individual interviews with students.We find that students share many common difficulties related to these concepts.Many students struggled to write a many-particle stationary state wavefunction consistent with the symmetrization requirements for the system, i.e., a completely antisymmetric wavefunction for a system of fermions or a completely symmetric wavefunction for a system of bosons.We discuss the common difficulties pertaining to these concepts that can be used as a guide to develop research-validated learning tools.

DOI
10.1119/perc.2020.pr.keebaugh

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We discuss an investigation of student difficulties with concepts related to the many-particle stationary state wavefunction for a system of non-interacting fermions or bosons in cases in which the many-particle stationary state wavefunction can be written as the product of the spatial and spin parts.The investigation was carried out in advanced quantum mechanics courses by administering free-response and multiple-choice questions and conducting individual interviews with students.We find that students share many common difficulties related to these concepts.Many students struggled to write a many-particle stationary state wavefunction consistent with the symmetrization requirements for the system, i.e., a completely antisymmetric wavefunction for a system of fermions or a completely symmetric wavefunction for a system of bosons.We discuss the common difficulties pertaining to these concepts that can be used as a guide to develop research-validated learning tools.
We discuss an investigation of upper-level undergraduate and graduate students' difficulties with fundamental concepts involving a system of identical particles.The investigation was carried out in advanced quantum mechanics courses by administering written questions and conducting individual interviews with students.We find that students share many common difficulties related to these quantum mechanical concepts, e.g., with regard to the many-particle Hamiltonian and stationary state wavefunctions for a system of non-interacting identical particles.
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.
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.