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written by Hunter G. Close, Catherine C. Schiber, Eleanor W. Close, and David Donnelly
Quantum states are traditionally cognitively managed exclusively with algebra rather than geometry. One reason for emphasizing algebra is the high dimensionality of quantum mathematical systems; even spin-1/2 systems require a 2-d complex number space for describing their quantum states, which can be hard to visualize. Using "nested phasor diagrams," which use nesting to increase the dimensionality of graphic space, we taught undergraduate students to represent spin-1/2 states graphically as well as algebraically. In oral exams, students were asked to identify which spin-1/2 states, expressed arithmetically, would generate the same set of probabilities as each other (i.e., they are the same except for a different overall phase factor). Video records of oral exams (N=13) show that no student performed this task successfully using an algebraic method; instead, all successful students solved the problem graphically. Furthermore, most students who were successful used a certain gesture to solve the problem.
Physics Education Research Conference 2013
Part of the PER Conference series
Portland, OR: July 17-18, 2013
Pages 93-96
Subjects Levels Resource Types
Education - Basic Research
- Problem Solving
= Representational Use
- Student Characteristics
= Skills
Quantum Physics
- Spin and Finite Dimensional Systems
- Upper Undergraduate
- Reference Material
= Research study
PER-Central Type Intended Users Ratings
- PER Literature
- Researchers
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Format:
application/pdf
Mirror:
http://dx.doi.org/10.1119/perc.20…
Access Rights:
Free access
License:
This material is released under a Creative Commons Attribution 3.0 license. Further distribution of this work must maintain attribution to the published article's author(s), title, proceedings citation, and DOI.
Rights Holder:
American Association of Physics Teachers
DOI:
10.1119/perc.2013.pr.011
PACSs:
01.40.Fk
01.40.Ha
03.65.Aa
Keywords:
PERC 2013, gesture, graphics, quantum mechanics, spatial cognition, spin
Record Cloner:
Metadata instance created January 29, 2014 by Lyle Barbato
Record Updated:
January 30, 2014 by Lyle Barbato
Last Update
when Cataloged:
December 16, 2013
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Record Link
AIP Format
H. Close, C. Schiber, E. Close, and D. Donnelly, presented at the Physics Education Research Conference 2013, Portland, OR, 2013, WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13115&DocID=3664).
AJP/PRST-PER
H. Close, C. Schiber, E. Close, and D. Donnelly, Students' dynamic geometric reasoning about quantum spin-1/2 states, presented at the Physics Education Research Conference 2013, Portland, OR, 2013, <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13115&DocID=3664>.
APA Format
Close, H., Schiber, C., Close, E., & Donnelly, D. (2013, July 17-18). Students' dynamic geometric reasoning about quantum spin-1/2 states. Paper presented at Physics Education Research Conference 2013, Portland, OR. Retrieved November 22, 2014, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13115&DocID=3664
Chicago Format
Close, H, C. Schiber, E. Close, and D. Donnelly. "Students' dynamic geometric reasoning about quantum spin-1/2 states." Paper presented at the Physics Education Research Conference 2013, Portland, OR, July 17-18, 2013. http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13115&DocID=3664 (accessed 22 November 2014).
MLA Format
Close, Hunter, Catherine Schiber, Eleanor Close, and Dave Donnelly. "Students' dynamic geometric reasoning about quantum spin-1/2 states." Physics Education Research Conference 2013. Portland, OR: 2013. 93-96 of PER Conference. 22 Nov. 2014 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13115&DocID=3664>.
BibTeX Export Format
@inproceedings{ Author = "Hunter Close and Catherine Schiber and Eleanor Close and Dave Donnelly", Title = {Students' dynamic geometric reasoning about quantum spin-1/2 states}, BookTitle = {Physics Education Research Conference 2013}, Pages = {93-96}, Address = {Portland, OR}, Series = {PER Conference}, Month = {July 17-18}, Year = {2013} }
Refer Export Format

%A Hunter Close
%A Catherine Schiber
%A Eleanor Close
%A Dave Donnelly
%T Students' dynamic geometric reasoning about quantum spin-1/2 states
%S PER Conference
%D July 17-18 2013
%P 93-96
%C Portland, OR
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13115&DocID=3664
%O Physics Education Research Conference 2013
%O July 17-18
%O application/pdf

EndNote Export Format

%0 Conference Proceedings
%A Close, Hunter
%A Schiber, Catherine
%A Close, Eleanor
%A Donnelly, Dave
%D July 17-18 2013
%T Students' dynamic geometric reasoning about quantum spin-1/2 states
%B Physics Education Research Conference 2013
%C Portland, OR
%P 93-96
%S PER Conference
%8 July 17-18
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=13115&DocID=3664


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