Superintegrability and higher order polynomial algebras

Marquette, Ian (2010) Superintegrability and higher order polynomial algebras. Journal of Physics A - Mathematical and Theoretical, 43 13: 135203-1-135203-15. doi:10.1088/1751-8113/43/13/135203


Author Marquette, Ian
Title Superintegrability and higher order polynomial algebras
Journal name Journal of Physics A - Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8113
1751-8121
Publication date 2010-03-10
Sub-type Article (original research)
DOI 10.1088/1751-8113/43/13/135203
Volume 43
Issue 13
Start page 135203-1
End page 135203-15
Total pages 15
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Abstract We present a method to obtain higher order integrals and polynomial algebras for two-dimensional quantum superintegrable systems separable in Cartesian coordinates from ladder operators. All systems with a second- and a third-order integral of motion separable in Cartesian coordinates were studied. The integrals of motion of two of them do not generate a cubic algebra. We construct for these Hamiltonians a higher order polynomial algebra from their ladder operators. We obtain quintic and seventh-order polynomial algebras. We also give for the polynomial algebras of order 7 realizations in terms of deformed oscillator algebras. These realizations and finite-dimensional unitary representations allow us to obtain the energy spectrum. We also apply the construction to the caged anisotropic harmonic oscillator and a system involving the fourth Painlevé transcendent.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 32 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 35 times in Scopus Article | Citations
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Created: Mon, 24 Oct 2011, 13:48:03 EST by Ian Marquette on behalf of Mathematics