Journal Article Detail Page
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
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Record Link
<a href="https://www.per-central.org/items/detail.cfm?ID=15628">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.</a>
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 November 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 November 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 Nov. 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 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
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The AIP Style presented is based on information from the AIP Style Manual. The AJP/PRST-PER presented is based on the AIP Style with the addition of journal article titles and conference proceeding article titles. The APA Style presented is based on information from APA Style.org: Electronic References. The Chicago Style presented is based on information from Examples of Chicago-Style Documentation. The MLA Style presented is based on information from the MLA FAQ. |
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