Probing student reasoning in relating relative phase and quantum phenomena

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students’ reasoning patterns in relating relative phases and real-world...

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Autores principales:	Tong Wan, Paul J. Emigh, Peter S. Shaffer
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2019
Materias:	Special aspects of education LC8-6691 Physics QC1-999
Acceso en línea:	https://doaj.org/article/7e839f726bc9443a9fe36879f21e43ed
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spelling	oai:doaj.org-article:7e839f726bc9443a9fe36879f21e43ed2021-12-02T16:20:38ZProbing student reasoning in relating relative phase and quantum phenomena10.1103/PhysRevPhysEducRes.15.0201392469-9896https://doaj.org/article/7e839f726bc9443a9fe36879f21e43ed2019-10-01T00:00:00Zhttp://doi.org/10.1103/PhysRevPhysEducRes.15.020139http://doi.org/10.1103/PhysRevPhysEducRes.15.020139https://doaj.org/toc/2469-9896In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students’ reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved one observational experiment and three testing experiments, during which we formulated and tested three hypotheses that allow us to gain insights into why students have difficulty recognizing the measurable effects of relative phases. We found that, in both spin-1/2 and infinite square well contexts, many students do not recognize that quantum states differing only by a relative phase are experimentally distinguishable. Moreover, student ability to recognize the measurable effects of relative phase does not improve when given (i) a task that specifically prompts students to compare the probabilities for a particular observable and (ii) a task that does not require taking inner products or changing basis. We also examined the extent to which lacking proficiency with complex numbers may have hindered student understanding of relative phase. The data indicate that most students are proficient with complex numbers. These findings suggest that many students do not, in fact, recognize the purpose of using complex numbers in superposition states. We discuss possible explanations for why students do not seem to recognize this purpose, and we also provide suggestions for future avenues of research.Tong WanPaul J. EmighPeter S. ShafferAmerican Physical SocietyarticleSpecial aspects of educationLC8-6691PhysicsQC1-999ENPhysical Review Physics Education Research, Vol 15, Iss 2, p 020139 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Special aspects of education LC8-6691 Physics QC1-999
spellingShingle	Special aspects of education LC8-6691 Physics QC1-999 Tong Wan Paul J. Emigh Peter S. Shaffer Probing student reasoning in relating relative phase and quantum phenomena
description	In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students’ reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved one observational experiment and three testing experiments, during which we formulated and tested three hypotheses that allow us to gain insights into why students have difficulty recognizing the measurable effects of relative phases. We found that, in both spin-1/2 and infinite square well contexts, many students do not recognize that quantum states differing only by a relative phase are experimentally distinguishable. Moreover, student ability to recognize the measurable effects of relative phase does not improve when given (i) a task that specifically prompts students to compare the probabilities for a particular observable and (ii) a task that does not require taking inner products or changing basis. We also examined the extent to which lacking proficiency with complex numbers may have hindered student understanding of relative phase. The data indicate that most students are proficient with complex numbers. These findings suggest that many students do not, in fact, recognize the purpose of using complex numbers in superposition states. We discuss possible explanations for why students do not seem to recognize this purpose, and we also provide suggestions for future avenues of research.
format	article
author	Tong Wan Paul J. Emigh Peter S. Shaffer
author_facet	Tong Wan Paul J. Emigh Peter S. Shaffer
author_sort	Tong Wan
title	Probing student reasoning in relating relative phase and quantum phenomena
title_short	Probing student reasoning in relating relative phase and quantum phenomena
title_full	Probing student reasoning in relating relative phase and quantum phenomena
title_fullStr	Probing student reasoning in relating relative phase and quantum phenomena
title_full_unstemmed	Probing student reasoning in relating relative phase and quantum phenomena
title_sort	probing student reasoning in relating relative phase and quantum phenomena
publisher	American Physical Society
publishDate	2019
url	https://doaj.org/article/7e839f726bc9443a9fe36879f21e43ed
work_keys_str_mv	AT tongwan probingstudentreasoninginrelatingrelativephaseandquantumphenomena AT pauljemigh probingstudentreasoninginrelatingrelativephaseandquantumphenomena AT petersshaffer probingstudentreasoninginrelatingrelativephaseandquantumphenomena
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Probing student reasoning in relating relative phase and quantum phenomena

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