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ERIC Number: EJ1432370
Record Type: Journal
Publication Date: 2024
Pages: 16
Abstractor: As Provided
ISBN: N/A
ISSN: N/A
EISSN: EISSN-2469-9896
Available Date: N/A
Student Understanding of Eigenvalue Equations in Quantum Mechanics: Symbolic Blending and Sensemaking Analysis
A. R. Piña; Zeynep Topdemir; John R. Thompson
Physical Review Physics Education Research, v20 n1 Article 010153 2024
As part of an effort to examine students' mathematical sensemaking (MSM) in a spins-first quantum mechanics course during the transition from discrete (spin) to continuous (position) systems, students were asked to construct an eigenvalue equation for a one-dimensional position operator. A subset of responses took the general form of an eigenvalue equation written in Dirac notation. Symbolic blending, a combination of symbolic forms and conceptual blending, as well as a categorical framework for MSM, were used in the analysis. The data suggest two different symbolic forms for an eigenvalue equation that share a symbol template but have distinct conceptual schemata: A transformation that reproduces the original and to operate is to act. These symbolic forms, when blended with two sets of contextual knowledge, form the basis of three different interpretations of eigenvalue equations modeled here as conceptual blends. The analysis in this study serves as a novel example of, and preliminary evidence for, student engagement in sensemaking activities in the transition from discrete to continuous systems in a spins-first quantum mechanics course.
American Physical Society. One Physics Ellipse 4th Floor, College Park, MD 20740-3844. Tel: 301-209-3200; Fax: 301-209-0865; e-mail: assocpub@aps.org; Web site: https://journals.aps.org/prper/
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF), Division of Physics (PHY)
Authoring Institution: N/A
Grant or Contract Numbers: 1912087
Author Affiliations: N/A