Fordy, AP orcid.org/0000-0002-2523-0262 (2018) Classical and Quantum Super-integrability: From Lissajous Figures to Exact Solvability. Physics of Atomic Nuclei, 81 (6). pp. 832-842. ISSN 1063-7788
Abstract
The first part of this paper explains what super-integrability is and how it differs in the classical and quantum cases. This is illustrated with an elementary example of the resonant harmonic oscillator. For Hamiltonians in “natural form”, the kinetic energy has geometric origins and, in the flat and constant curvature cases, the large isometry group plays a vital role. We explain how to use the corresponding first integrals to build separable and super-integrable systems. We also show how to use the automorphisms of the symmetry algebra to help build the Poisson relations of the corresponding non–Abelian Poisson algebra. Finally, we take both the classical and quantum Zernike system, recently discussed by Pogosyan et al., and show how the algebraic structure of its super-integrability can be understood in this framework.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Pleiades Publishing, Ltd. 2018. This is an author produced version of a paper published in Physics of Atomic Nuclei. Uploaded in accordance with the publisher's self-archiving policy. The final, published version can be found at: https://doi.org/10.1134/S1063778818060133 |
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: | 09 Jul 2018 10:54 |
Last Modified: | 04 Mar 2019 11:45 |
Status: | Published |
Publisher: | Pleiades Publishing |
Identification Number: | 10.1134/S1063778818060133 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132974 |