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Graduate Student Misunderstandings of Wave Functions in an Asymmetric Well

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Title: Graduate Student Misunderstandings of Wave Functions in an Asymmetric Well
Language: English
Authors: Porter, C. D., Heckler, A.F
Source: Physical Review Physics Education Research. Jan-Jun 2019 15(1).
Availability: American Physical Society. One Physics Ellipse 4th Floor, College Park, MD 20740-3844. Tel: 301-209-3200; Fax: 301-209-0865; e-mail: assocpub@aps.org; Web site: http://prst-per.aps.org
Peer Reviewed: Y
Page Count: 10
Publication Date: 2019
Sponsoring Agency: National Science Foundation (NSF)
Contract Number: 1735027
DMR1420451
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Graduate Students, Student Attitudes, Misconceptions, Quantum Mechanics, Physics, Science Instruction, Scientific Concepts, Probability, Energy, Pretests Posttests
Geographic Terms: Ohio (Columbus)
DOI: 10.1103/PhysRevPhysEducRes.15.010139
ISSN: 2469-9896
Abstract: Quantum mechanics is a notoriously counterintuitive subject within physics and has been the subject of a number of studies at the undergraduate level, and a few pioneering studies at the graduate level. The sketching of wave functions in a confining well is in one sense one of the most basic activities in quantum mechanics. But in another sense, it may be viewed as a rather advanced skill, as it requires the coherent inclusion of a number of details of the wave function, such as wavelength, probability amplitude, and boundary conditions, among others. Although sketching a wave function is not a common activity at the graduate level, a great deal of graduate work is concerned with the aforementioned details, especially boundary conditions. Whether it is seen as a basic skill, or as linked to higher-level understanding, sketching a wave function is an ability that physics graduate students should have. Here, we report on graduate students' ability to sketch wave functions in an asymmetric potential well. We find that the frequency of many errors is not significantly reduced from pretest to posttest, meaning that many errors persist through to the end of graduate quantum mechanics instruction. We find that only 5% of graduate students tested can sketch the 2nd excited state wave function without errors. We include quantitative and diagrammatic descriptions of student errors covering a broader range of misunderstandings than has previously been identified, and we include interview information that speaks to the persistence of some of the errors.
Abstractor: As Provided
Entry Date: 2019
Accession Number: EJ1221054
Database: ERIC
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  Data: American Physical Society. One Physics Ellipse 4th Floor, College Park, MD 20740-3844. Tel: 301-209-3200; Fax: 301-209-0865; e-mail: assocpub@aps.org; Web site: http://prst-per.aps.org
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  Data: 10.1103/PhysRevPhysEducRes.15.010139
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  Data: Quantum mechanics is a notoriously counterintuitive subject within physics and has been the subject of a number of studies at the undergraduate level, and a few pioneering studies at the graduate level. The sketching of wave functions in a confining well is in one sense one of the most basic activities in quantum mechanics. But in another sense, it may be viewed as a rather advanced skill, as it requires the coherent inclusion of a number of details of the wave function, such as wavelength, probability amplitude, and boundary conditions, among others. Although sketching a wave function is not a common activity at the graduate level, a great deal of graduate work is concerned with the aforementioned details, especially boundary conditions. Whether it is seen as a basic skill, or as linked to higher-level understanding, sketching a wave function is an ability that physics graduate students should have. Here, we report on graduate students' ability to sketch wave functions in an asymmetric potential well. We find that the frequency of many errors is not significantly reduced from pretest to posttest, meaning that many errors persist through to the end of graduate quantum mechanics instruction. We find that only 5% of graduate students tested can sketch the 2nd excited state wave function without errors. We include quantitative and diagrammatic descriptions of student errors covering a broader range of misunderstandings than has previously been identified, and we include interview information that speaks to the persistence of some of the errors.
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      – SubjectFull: Graduate Students
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      – SubjectFull: Student Attitudes
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      – SubjectFull: Misconceptions
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      – SubjectFull: Pretests Posttests
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      – SubjectFull: Ohio (Columbus)
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