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Physical Review Physics Education Research
written by Tao Tu, Chuan-Feng Li, Chuan-Feng Zhou, and Guang-Can Guo
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.
Physical Review Physics Education Research: Volume 16, Issue 2, Pages 020163
Subjects Levels Resource Types
Education - Basic Research
- Achievement
- Problem Solving
= Processes
- Research Design & Methodology
= Data
= Statistics
- Student Characteristics
= Ability
Mathematical Tools
- Differential Equations
Other Sciences
- Mathematics
Quantum Physics
- General
- Upper Undergraduate
- Reference Material
= Research study
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This material is released under a Creative Commons Attribution 4.0 license.
Rights Holder:
American Physical Society
DOI:
10.1103/PhysRevPhysEducRes.16.020163
Keywords:
ACER, mathematics applications
Record Creator:
Metadata instance created May 12, 2021 by Bruce Mason
Record Updated:
October 27, 2022 by Caroline Hall
Last Update
when Cataloged:
December 21, 2020
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AIP Format
T. Tu, C. Li, C. Zhou, and G. Guo, , Phys. Rev. Phys. Educ. Res. 16 (2), 020163 (2020), WWW Document, (https://doi.org/10.1103/PhysRevPhysEducRes.16.020163).
AJP/PRST-PER
T. Tu, C. Li, C. Zhou, and G. Guo, Students’ difficulties with partial differential equations in quantum mechanics, Phys. Rev. Phys. Educ. Res. 16 (2), 020163 (2020), <https://doi.org/10.1103/PhysRevPhysEducRes.16.020163>.
APA Format
Tu, T., Li, C., Zhou, C., & Guo, G. (2020, December 21). Students’ difficulties with partial differential equations in quantum mechanics. Phys. Rev. Phys. Educ. Res., 16(2), 020163. Retrieved June 12, 2024, from https://doi.org/10.1103/PhysRevPhysEducRes.16.020163
Chicago Format
Tu, T, C. Li, C. Zhou, and G. Guo. "Students’ difficulties with partial differential equations in quantum mechanics." Phys. Rev. Phys. Educ. Res. 16, no. 2, (December 21, 2020): 020163, https://doi.org/10.1103/PhysRevPhysEducRes.16.020163 (accessed 12 June 2024).
MLA Format
Tu, Tao, Chuan-Feng Li, Chuan-Feng Zhou, and Guang-Can Guo. "Students’ difficulties with partial differential equations in quantum mechanics." Phys. Rev. Phys. Educ. Res. 16.2 (2020): 020163. 12 June 2024 <https://doi.org/10.1103/PhysRevPhysEducRes.16.020163>.
BibTeX Export Format
@article{ Author = "Tao Tu and Chuan-Feng Li and Chuan-Feng Zhou and Guang-Can Guo", Title = {Students’ difficulties with partial differential equations in quantum mechanics}, Journal = {Phys. Rev. Phys. Educ. Res.}, Volume = {16}, Number = {2}, Pages = {020163}, Month = {December}, Year = {2020} }
Refer Export Format

%A Tao Tu %A Chuan-Feng Li %A Chuan-Feng Zhou %A Guang-Can Guo %T Students' difficulties with partial differential equations in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 16 %N 2 %D December 21, 2020 %P 020163 %U https://doi.org/10.1103/PhysRevPhysEducRes.16.020163 %O application/pdf

EndNote Export Format

%0 Journal Article %A Tu, Tao %A Li, Chuan-Feng %A Zhou, Chuan-Feng %A Guo, Guang-Can %D December 21, 2020 %T Students' difficulties with partial differential equations in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 16 %N 2 %P 020163 %8 December 21, 2020 %U https://doi.org/10.1103/PhysRevPhysEducRes.16.020163


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