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Physical Review Physics Education Research
written by Tao Tu, Chuan-Feng Li, Jin-Shi Xu, and Guang-Can Guo
In the context of quantum mechanics, students are often asked to use delta functions to solve problems. Here, we investigate three typical problem-solving processes using delta functions: a delta function potential well problem, a position space delta function problem, and a momentum space delta function problem. We studied students' solutions in written exams and conducted think-aloud interviews. We use the activation, construction, execution, and reflection framework for our analysis. We find that students encountered various difficulties in solving quantum mechanics problems using delta functions. Common challenges included difficulty with establishing expressions of delta functions for position eigenstates, difficulty with expressing the orthonormality of eigenfunctions with continuous spectra using delta functions, difficulty with boundary conditions for delta function potentials, and difficulty with calculating integrals involved delta functions. In particular, students rarely used effective reflective methods to gain confidence in their solutions. We commonly observed this challenge for students in all questions we investigated. In addition, we compare the similarities and differences in the use of delta functions in electrostatics and in quantum mechanics, and discuss possible explanations for the reasoning mechanisms that cause these difficulties. Finally, we discuss the potential pedagogical implications of our findings.
Physical Review Physics Education Research: Volume 19, Issue 1, Pages 010104
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Free access
License:
This material is released under a Creative Commons Attribution 4.0 license.
Rights Holder:
American Physical Society
DOI:
10.1103/PhysRevPhysEducRes.19.010104
Keywords:
ACER framework, ACER problem-solving, Quantum mechanics pedagogy, eigenstates, quantum boundary conditions
Record Creator:
Metadata instance created February 28, 2023 by Lyle Barbato
Record Updated:
March 21, 2023 by Caroline Hall
Last Update
when Cataloged:
February 1, 2023
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AIP Format
T. Tu, C. Li, J. Xu, and G. Guo, , Phys. Rev. Phys. Educ. Res. 19 (1), 010104 (2023), WWW Document, (https://doi.org/10.1103/PhysRevPhysEducRes.19.010104).
AJP/PRST-PER
T. Tu, C. Li, J. Xu, and G. Guo, Students’ difficulties with the Dirac delta function in quantum mechanics, Phys. Rev. Phys. Educ. Res. 19 (1), 010104 (2023), <https://doi.org/10.1103/PhysRevPhysEducRes.19.010104>.
APA Format
Tu, T., Li, C., Xu, J., & Guo, G. (2023, February 1). Students’ difficulties with the Dirac delta function in quantum mechanics. Phys. Rev. Phys. Educ. Res., 19(1), 010104. Retrieved July 22, 2024, from https://doi.org/10.1103/PhysRevPhysEducRes.19.010104
Chicago Format
Tu, T, C. Li, J. Xu, and G. Guo. "Students’ difficulties with the Dirac delta function in quantum mechanics." Phys. Rev. Phys. Educ. Res. 19, no. 1, (February 1, 2023): 010104, https://doi.org/10.1103/PhysRevPhysEducRes.19.010104 (accessed 22 July 2024).
MLA Format
Tu, Tao, Chuan-Feng Li, Jin-Shi Xu, and Guang-Can Guo. "Students’ difficulties with the Dirac delta function in quantum mechanics." Phys. Rev. Phys. Educ. Res. 19.1 (2023): 010104. 22 July 2024 <https://doi.org/10.1103/PhysRevPhysEducRes.19.010104>.
BibTeX Export Format
@article{ Author = "Tao Tu and Chuan-Feng Li and Jin-Shi Xu and Guang-Can Guo", Title = {Students’ difficulties with the Dirac delta function in quantum mechanics}, Journal = {Phys. Rev. Phys. Educ. Res.}, Volume = {19}, Number = {1}, Pages = {010104}, Month = {February}, Year = {2023} }
Refer Export Format

%A Tao Tu %A Chuan-Feng Li %A Jin-Shi Xu %A Guang-Can Guo %T Students' difficulties with the Dirac delta function in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 19 %N 1 %D February 1, 2023 %P 010104 %U https://doi.org/10.1103/PhysRevPhysEducRes.19.010104 %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 February 1, 2023 %T Students' difficulties with the Dirac delta function in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 19 %N 1 %P 010104 %8 February 1, 2023 %U https://doi.org/10.1103/PhysRevPhysEducRes.19.010104


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