Fordy, AP orcid.org/0000-0002-2523-0262 (2020) The role of commuting operators in quantum superintegrable systems. Journal of Physics A: Mathematical and Theoretical, 53 (35). 354001. p. 354001. ISSN 1751-8113
Abstract
We discuss the role of commuting operators for quantum superintegrable systems, showing how they are used to build eigenfunctions. These ideas are illustrated in the context of resonant harmonic oscillators, the Krall–Sheffer operators, with polynomial eigenfunctions, and the Calogero–Moser system with additional harmonic potential. The construction is purely algebraic, avoiding the use of separation of variables and differential equation theory.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/ab9edd. |
Keywords: | orthogonal polynomials in two variables; recurrence relations; ladder operators; quantum integrable systems; super-integrability |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Aug 2020 15:29 |
Last Modified: | 22 Jun 2021 00:38 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1751-8121/ab9edd |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:164363 |