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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.
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Student Understanding of Eigenvalue Equations in Quantum Mechanics: Symbolic Forms Analysis
As part of an effort to examine students’ mathematical sensemaking (MSM) in a spins-first quantum mechanics (QM) course, students were asked to construct an eigenvalue equation (EE) for a one-dimensional position operator. Sherin’s symbolic forms were used in analysis. The data suggest three symbolic forms for an EE, all sharing a single symbol template but with unique conceptual schemata: a transformation which reproduces the original, an operation taking a measurement of state, and a statement about the potential results of measurement. These findings corroborate prior literature on a construction task rather than a comparison or deconstruction task, and with a continuous variable after instruction on discrete variables.
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- Award ID(s):
- 1912087
- PAR ID:
- 10535973
- Publisher / Repository:
- Mathematical Association of America
- Date Published:
- ISSN:
- 2474-9346
- Page Range / eLocation ID:
- 90-98
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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