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1.
Representation issues: Using mathematics in upper-division physics
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J. Wagner, C. Manogue, and J. Thompson, PERC 2011 Proceedings, 89-92.
Upper-division students must learn to apply sophisticated mathematics from algebra, limits, calculus, multivariable and vector calculus, linear algebra, complex variables, and…
https://www.per-central.org/document/ServeFile.cfm?ID=11820&DocID=2670
2.
Investigating Student Difficulties with Dirac Notation
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C. Singh and E. Marshman, PERC 2013 Proceedings, 345-348.
Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been…
https://www.per-central.org/document/ServeFile.cfm?ID=13149&DocID=3696
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Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations
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E. Marshman and C. Singh, PERC 2015 Proceedings, 211-214.
Dirac notation is often used in upper level quantum mechanics courses, but students struggle with this representation. To investigate the difficulties that advanced students (i.e.,…
https://www.per-central.org/document/ServeFile.cfm?ID=13873&DocID=4291
4.
Investigating Student Understanding of Perturbation Theory and the Inner Products of Functions
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G. Passante, P. Emigh, T. Wan, and P. Shaffer, PERC 2015 Proceedings, 247-250.
We have investigated the extent to which students can qualitatively determine the effect of perturbations to a Hamiltonian on the energies of the eigenfunctions. The results indicate…
https://www.per-central.org/document/ServeFile.cfm?ID=13883&DocID=4301
5.
Student difficulties with representations of quantum operators corresponding to observables
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E. Marshman and C. Singh, PERC 2016 Proceedings, 216-219.
Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum…
https://www.per-central.org/document/ServeFile.cfm?ID=14232&DocID=4586
6.
How students apply linear algebra to quantum mechanics
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C. Hillebrand-Viljoen and S. Wheaton, PERC 2018 Proceedings.
This paper describes a framework for how students apply linear algebra to quantum mechanics based on a survey of 61 students at various levels. The framework divides mathematics into…
https://www.per-central.org/document/ServeFile.cfm?ID=14797&DocID=4944
7.
Student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect
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E. Marshman, C. Keebaugh, and C. Singh, PERC 2018 Proceedings.
We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect using the degenerate…
https://www.per-central.org/document/ServeFile.cfm?ID=14821&DocID=4968
8.
Examining student understanding of matrix algebra and eigentheory
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P. Her and M. Loverude, PERC 2020 Proceedings, 210-215.
Matrix algebra and eigentheory are important to students’ learning of physics in upper division physics courses. In this study, we investigated how students apply matrix algebra and…
https://www.per-central.org/document/ServeFile.cfm?ID=15485&DocID=5333
