The role of commuting operators in quantum superintegrable systems

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

Authors/Creators:	Fordy, AP https://orcid.org/0000-0002-2523-0262
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:	Accepted: 22 June 2020 Published (online): 22 June 2020 Published: 4 September 2020
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:	https://doi.org/10.1088/1751-8121/ab9edd

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The role of commuting operators in quantum superintegrable systems

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