Using Mathematics to Inform Conceptual Reasoning about Quantum Tunneling

Mathematics

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Scientific paper

Previously, we have reported on work at the University of Maine investigating how undergraduate physics students reason about the phenomenon of quantum mechanical tunneling.(1) The majority of our interview sessions involved a series of qualitative questions regarding a square-barrier tunneling scenario. For a select group of students, we began second interview sessions by asking them to solve the time-independent Schrodinger equation prior to answering a series of conceptual questions. All were able to produce reasonably correct solutions, which could be used throughout the interview to reason about the answers to many of our questions. However, in several instances students either failed to refer to the mathematics when responding, or seemed to struggle with understanding their equations and how the mathematics informed the correct responses, suggesting a discontinuity between their mathematical reasoning and their physical reasoning.
1. M. C. Wittman, J. T. Morgan, and L. Bao. Addressing student models of energy loss in quantum tunneling. Eur. J. Phys. 26, 939-950 (2005).

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