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Physical Review Physics Education Research
written by Benjamin P. Schermerhorn, Giaco Corsiglia, Homeyra R. Sadaghiani, Gina Passante, and Steven J. Pollock
We conducted a multiyear project across three institutions to develop an instructional tutorial that supports student understanding of change of basis in quantum mechanics. Building from our previous work, we identified learning goals to guide activity development. The tutorial makes an analogy between spin-1/2 states and a Cartesian coordinate system. This paper details the iterative development process including reports of observations from classroom implementations and the resulting modifications to the activity. Further, we report preliminary findings on the success of the activity in improving students' ability to correctly change basis and their articulation that change of basis is a choice of representation, not a change to the physical system.
Physical Review Physics Education Research: Volume 18, Issue 1, Pages 010145
Subjects Levels Resource Types
Education - Applied Research
- Active Learning
= Problem Solving
- Curriculum Development
- Instructional Material Design
= Tutorial
Education - Basic Research
- Learning Theory
= Cognitive Apprenticeship
- Problem Solving
= Frameworks
- Student Characteristics
= Ability
= Affect
= Skills
Quantum Physics
- Approximation Techniques
- Bound State Systems
= Finite Well
= Infinite Well
- Entanglement and Quantum Information
- Foundations and Measurements
= Hilbert Space
- Upper Undergraduate
- Reference Material
= Research study
PER-Central Type Intended Users Ratings
- PER Literature
- Professional/Practitioners
- Administrators
- Researchers
- Educators
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Access Rights:
Free access
License:
This material is released under a Creative Commons Attribution 4.0 license.
Rights Holder:
American Physical Society
DOI:
10.1103/PhysRevPhysEducRes.18.010145
NSF Numbers:
DUE-1626280
DUE-1626594
DUE-1626482
Keywords:
QBT curriculum, QBT teaching method, Quantum Basis Tutorials, Spin 1/2 systems, Spins First curriculum, context-rich problems
Record Creator:
Metadata instance created June 28, 2022 by Lyle Barbato
Record Updated:
July 21, 2023 by Caroline Hall
Last Update
when Cataloged:
June 8, 2022
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Record Link
AIP Format
B. Schermerhorn, G. Corsiglia, H. Sadaghiani, G. Passante, and S. Pollock, , Phys. Rev. Phys. Educ. Res. 18 (1), 010145 (2022), WWW Document, (https://doi.org/10.1103/PhysRevPhysEducRes.18.010145).
AJP/PRST-PER
B. Schermerhorn, G. Corsiglia, H. Sadaghiani, G. Passante, and S. Pollock, From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics, Phys. Rev. Phys. Educ. Res. 18 (1), 010145 (2022), <https://doi.org/10.1103/PhysRevPhysEducRes.18.010145>.
APA Format
Schermerhorn, B., Corsiglia, G., Sadaghiani, H., Passante, G., & Pollock, S. (2022, June 8). From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics. Phys. Rev. Phys. Educ. Res., 18(1), 010145. Retrieved December 5, 2024, from https://doi.org/10.1103/PhysRevPhysEducRes.18.010145
Chicago Format
Schermerhorn, B, G. Corsiglia, H. Sadaghiani, G. Passante, and S. Pollock. "From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics." Phys. Rev. Phys. Educ. Res. 18, no. 1, (June 8, 2022): 010145, https://doi.org/10.1103/PhysRevPhysEducRes.18.010145 (accessed 5 December 2024).
MLA Format
Schermerhorn, Benjamin P., Giaco Corsiglia, Homeyra Sadaghiani, Gina Passante, and Steven Pollock. "From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics." Phys. Rev. Phys. Educ. Res. 18.1 (2022): 010145. 5 Dec. 2024 <https://doi.org/10.1103/PhysRevPhysEducRes.18.010145>.
BibTeX Export Format
@article{ Author = "Benjamin P. Schermerhorn and Giaco Corsiglia and Homeyra Sadaghiani and Gina Passante and Steven Pollock", Title = {From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics}, Journal = {Phys. Rev. Phys. Educ. Res.}, Volume = {18}, Number = {1}, Pages = {010145}, Month = {June}, Year = {2022} }
Refer Export Format

%A Benjamin P. Schermerhorn %A Giaco Corsiglia %A Homeyra Sadaghiani %A Gina Passante %A Steven Pollock %T From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 18 %N 1 %D June 8, 2022 %P 010145 %U https://doi.org/10.1103/PhysRevPhysEducRes.18.010145 %O application/pdf

EndNote Export Format

%0 Journal Article %A Schermerhorn, Benjamin P. %A Corsiglia, Giaco %A Sadaghiani, Homeyra %A Passante, Gina %A Pollock, Steven %D June 8, 2022 %T From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics %J Phys. Rev. Phys. Educ. Res. %V 18 %N 1 %P 010145 %8 June 8, 2022 %U https://doi.org/10.1103/PhysRevPhysEducRes.18.010145


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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.

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From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics:

Is Associated With Exploring student ideas on change of basis in quantum mechanics

A research study that addresses the same topic (understanding basis in quantum mechanics), and was conducted in the same university settings.

relation by Caroline Hall

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