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Physical Review Physics Education Research
written by Tao Tu, Chuan-Feng Li, Jin-Shi Xu, and Guang-Can Guo
In quantum mechanics courses, students are often asked to solve bound and scattering state problems. The use of an ordinary differential equation is a standard technique to solve these questions. Here, we investigated students' problem-solving processes for two typical problems of a single particle in one spatial dimension: a bound state problem and a scattering state problem. We analyzed students' solutions to written exams and utilized think-aloud interviews using a framework that includes four stages: activation, construction, execution, and reflection. We found that the students encountered various difficulties when they solved the ordinary differential equations to obtain the properties of bound or scattering states. Common difficulties included recognizing when the time-dependent Schrödinger equation is the appropriate model; selecting a range of the energy constants that satisfies the bound or scattering state; justifying when to use a superposition form of the wave functions; grasping the physical definition of scattering coefficients; and using an effective checking method for their solutions. In addition, we observed qualitatively different difficulties in students' solutions to the two problems and discussed possible explanations for the underlying reasoning mechanisms that cause these difficulties. Finally, we discussed the potential implications of our findings for instruction.
Physical Review Physics Education Research: Volume 17, Issue 2, Pages 020142
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Free access
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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.17.020142
Keywords:
cognitive theory, epistemology, quantum mechanics pedagogy, quantum physics pedagogy, schema
Record Creator:
Metadata instance created December 28, 2021 by Lyle Barbato
Record Updated:
January 25, 2022 by Lyle Barbato
Last Update
when Cataloged:
December 14, 2021
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AIP Format
T. Tu, C. Li, J. Xu, and G. Guo, , Phys. Rev. Phys. Educ. Res. 17 (2), 020142 (2021), WWW Document, (https://doi.org/10.1103/PhysRevPhysEducRes.17.020142).
AJP/PRST-PER
T. Tu, C. Li, J. Xu, and G. Guo, Students’ difficulties with solving bound and scattering state problems in quantum mechanics, Phys. Rev. Phys. Educ. Res. 17 (2), 020142 (2021), <https://doi.org/10.1103/PhysRevPhysEducRes.17.020142>.
APA Format
Tu, T., Li, C., Xu, J., & Guo, G. (2021, December 14). Students’ difficulties with solving bound and scattering state problems in quantum mechanics. Phys. Rev. Phys. Educ. Res., 17(2), 020142. Retrieved April 16, 2024, from https://doi.org/10.1103/PhysRevPhysEducRes.17.020142
Chicago Format
Tu, T, C. Li, J. Xu, and G. Guo. "Students’ difficulties with solving bound and scattering state problems in quantum mechanics." Phys. Rev. Phys. Educ. Res. 17, no. 2, (December 14, 2021): 020142, https://doi.org/10.1103/PhysRevPhysEducRes.17.020142 (accessed 16 April 2024).
MLA Format
Tu, Tao, Chuan-Feng Li, Jin-Shi Xu, and Guang-Can Guo. "Students’ difficulties with solving bound and scattering state problems in quantum mechanics." Phys. Rev. Phys. Educ. Res. 17.2 (2021): 020142. 16 Apr. 2024 <https://doi.org/10.1103/PhysRevPhysEducRes.17.020142>.
BibTeX Export Format
@article{ Author = "Tao Tu and Chuan-Feng Li and Jin-Shi Xu and Guang-Can Guo", Title = {Students’ difficulties with solving bound and scattering state problems in quantum mechanics}, Journal = {Phys. Rev. Phys. Educ. Res.}, Volume = {17}, Number = {2}, Pages = {020142}, Month = {December}, Year = {2021} }
Refer Export Format

%A Tao Tu %A Chuan-Feng Li %A Jin-Shi Xu %A Guang-Can Guo %T Students' difficulties with solving bound and scattering state problems in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 17 %N 2 %D December 14, 2021 %P 020142 %U https://doi.org/10.1103/PhysRevPhysEducRes.17.020142 %O application/pdf

EndNote Export Format

%0 Journal Article %A Tu, Tao %A Li, Chuan-Feng %A Xu, Jin-Shi %A Guo, Guang-Can %D December 14, 2021 %T Students' difficulties with solving bound and scattering state problems in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 17 %N 2 %P 020142 %8 December 14, 2021 %U https://doi.org/10.1103/PhysRevPhysEducRes.17.020142


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