Students’ difficulties with partial differential equations in quantum mechanics

Upper-division physics students solve partial differential equations in various contexts in quantum mechanics courses. Separation of variables is a standard technique to solve these equations. We investigated students’ solutions to midterm exam questions and utilized think-aloud interviews. We also...

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Autores principales:	Tao Tu, Chuan-Feng Li, Zong-Quan Zhou, Guang-Can Guo
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Special aspects of education LC8-6691 Physics QC1-999
Acceso en línea:	https://doaj.org/article/1a9e405f70a943bdbd67befb63a2bf0f
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spelling	oai:doaj.org-article:1a9e405f70a943bdbd67befb63a2bf0f2021-12-02T13:27:25ZStudents’ difficulties with partial differential equations in quantum mechanics10.1103/PhysRevPhysEducRes.16.0201632469-9896https://doaj.org/article/1a9e405f70a943bdbd67befb63a2bf0f2020-12-01T00:00:00Zhttp://doi.org/10.1103/PhysRevPhysEducRes.16.020163http://doi.org/10.1103/PhysRevPhysEducRes.16.020163https://doaj.org/toc/2469-9896Upper-division physics students solve partial differential equations in various contexts in quantum mechanics courses. Separation of variables is a standard technique to solve these equations. We investigated students’ solutions to midterm exam questions and utilized think-aloud interviews. We also applied a framework that organizes students’ problem-solving process into four stages: activate, construct, execute, and reflect. Here we focused on students’ problem-solving process for two typical problems in the context of quantum mechanics: an energy eigenfunction problem in two spatial dimensions and a time evolution problem in one spatial dimension. We found that the students encountered various difficulties when they used the separation of variables technique to solve these partial differential equations. Common difficulties included recognizing when separation of variables is the appropriate method, deriving the correct separated equations from the original equation, deciding the signs of the separation constants, justifying when using the summation form of the wave function, and using an effective reflecting tool for their final solutions. In addition, we observed qualitatively and quantitatively different errors in students’ solutions to the two problems. Finally, we discussed the possible implications of our findings for instruction.Tao TuChuan-Feng LiZong-Quan ZhouGuang-Can GuoAmerican Physical SocietyarticleSpecial aspects of educationLC8-6691PhysicsQC1-999ENPhysical Review Physics Education Research, Vol 16, Iss 2, p 020163 (2020)
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 Tao Tu Chuan-Feng Li Zong-Quan Zhou Guang-Can Guo Students’ difficulties with partial differential equations in quantum mechanics
description	Upper-division physics students solve partial differential equations in various contexts in quantum mechanics courses. Separation of variables is a standard technique to solve these equations. We investigated students’ solutions to midterm exam questions and utilized think-aloud interviews. We also applied a framework that organizes students’ problem-solving process into four stages: activate, construct, execute, and reflect. Here we focused on students’ problem-solving process for two typical problems in the context of quantum mechanics: an energy eigenfunction problem in two spatial dimensions and a time evolution problem in one spatial dimension. We found that the students encountered various difficulties when they used the separation of variables technique to solve these partial differential equations. Common difficulties included recognizing when separation of variables is the appropriate method, deriving the correct separated equations from the original equation, deciding the signs of the separation constants, justifying when using the summation form of the wave function, and using an effective reflecting tool for their final solutions. In addition, we observed qualitatively and quantitatively different errors in students’ solutions to the two problems. Finally, we discussed the possible implications of our findings for instruction.
format	article
author	Tao Tu Chuan-Feng Li Zong-Quan Zhou Guang-Can Guo
author_facet	Tao Tu Chuan-Feng Li Zong-Quan Zhou Guang-Can Guo
author_sort	Tao Tu
title	Students’ difficulties with partial differential equations in quantum mechanics
title_short	Students’ difficulties with partial differential equations in quantum mechanics
title_full	Students’ difficulties with partial differential equations in quantum mechanics
title_fullStr	Students’ difficulties with partial differential equations in quantum mechanics
title_full_unstemmed	Students’ difficulties with partial differential equations in quantum mechanics
title_sort	students’ difficulties with partial differential equations in quantum mechanics
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/1a9e405f70a943bdbd67befb63a2bf0f
work_keys_str_mv	AT taotu studentsdifficultieswithpartialdifferentialequationsinquantummechanics AT chuanfengli studentsdifficultieswithpartialdifferentialequationsinquantummechanics AT zongquanzhou studentsdifficultieswithpartialdifferentialequationsinquantummechanics AT guangcanguo studentsdifficultieswithpartialdifferentialequationsinquantummechanics
_version_	1718392958932221952

Students’ difficulties with partial differential equations in quantum mechanics

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