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Physical Review Special Topics - Physics Education Research
written by Bethany R. Wilcox and Steven J. Pollock
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them. To characterize student difficulties with the delta function at the upper-division level, we examined students' responses to traditional exam questions and a standardized conceptual assessment, and conducted think-aloud interviews. Our analysis was guided by an analytical framework that focuses on how students activate, construct, execute, and reflect on the Dirac delta function in the context of problem solving in physics. Here, we focus on student difficulties using the delta function to express charge distributions in the context of junior-level electrostatics. Common challenges included invoking the delta function spontaneously, translating a description of a charge distribution into a mathematical expression using delta functions, integrating 3D or non-Cartesian delta function expressions, and recognizing that the delta function can have units. We also briefly discuss implications of these difficulties for instruction.
Subjects Levels Resource Types
Mathematical Tools
- Calculus
= Derivative
Other Sciences
- Mathematics
- Upper Undergraduate
- Reference Material
= Research study
PER-Central Type Intended Users Ratings
- PER Literature
- Educators
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- Researchers
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Formats:
application/pdf
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Access Rights:
Free access
License:
This material is released under a Creative Commons Attribution 3.0 license.
Rights Holder:
American Physical Society
DOI:
10.1103/PhysRevSTPER.11.010108
NSF Numbers:
DUE-1023028
DGE-1144083
Keywords:
Dirac equation, differential calculus
Record Creator:
Metadata instance created July 27, 2015 by Lyle Barbato
Record Updated:
June 15, 2022 by Caroline Hall
Last Update
when Cataloged:
March 9, 2015
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Record Link
AIP Format
B. Wilcox and S. Pollock, , Phys. Rev. ST Phys. Educ. Res. 11 (1), 010108 (2015), WWW Document, (https://doi.org/10.1103/PhysRevSTPER.11.010108).
AJP/PRST-PER
B. Wilcox and S. Pollock, Upper-division student difficulties with the Dirac delta function, Phys. Rev. ST Phys. Educ. Res. 11 (1), 010108 (2015), <https://doi.org/10.1103/PhysRevSTPER.11.010108>.
APA Format
Wilcox, B., & Pollock, S. (2015, March 9). Upper-division student difficulties with the Dirac delta function. Phys. Rev. ST Phys. Educ. Res., 11(1), 010108. Retrieved July 25, 2024, from https://doi.org/10.1103/PhysRevSTPER.11.010108
Chicago Format
Wilcox, Bethany, and Steven Pollock. "Upper-division student difficulties with the Dirac delta function." Phys. Rev. ST Phys. Educ. Res. 11, no. 1, (March 9, 2015): 010108, https://doi.org/10.1103/PhysRevSTPER.11.010108 (accessed 25 July 2024).
MLA Format
Wilcox, Bethany, and Steven Pollock. "Upper-division student difficulties with the Dirac delta function." Phys. Rev. ST Phys. Educ. Res. 11.1 (2015): 010108. 25 July 2024 <https://doi.org/10.1103/PhysRevSTPER.11.010108>.
BibTeX Export Format
@article{ Author = "Bethany Wilcox and Steven Pollock", Title = {Upper-division student difficulties with the Dirac delta function}, Journal = {Phys. Rev. ST Phys. Educ. Res.}, Volume = {11}, Number = {1}, Pages = {010108}, Month = {March}, Year = {2015} }
Refer Export Format

%A Bethany Wilcox %A Steven Pollock %T Upper-division student difficulties with the Dirac delta function %J Phys. Rev. ST Phys. Educ. Res. %V 11 %N 1 %D March 9, 2015 %P 010108 %U https://doi.org/10.1103/PhysRevSTPER.11.010108 %O application/pdf

EndNote Export Format

%0 Journal Article %A Wilcox, Bethany %A Pollock, Steven %D March 9, 2015 %T Upper-division student difficulties with the Dirac delta function %J Phys. Rev. ST Phys. Educ. Res. %V 11 %N 1 %P 010108 %8 March 9, 2015 %U https://doi.org/10.1103/PhysRevSTPER.11.010108


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