Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painleve transcendent potentials

Marquette, Ian (2009) Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painleve transcendent potentials. Journal of Mathematical Physics, 50 9: 095202-1-095202-18. doi:10.1063/1.3096708

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Author Marquette, Ian
Title Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painleve transcendent potentials
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
1527-2427
Publication date 2009-04-01
Year available 2009
Sub-type Article (original research)
DOI 10.1063/1.3096708
Open Access Status File (Publisher version)
Volume 50
Issue 9
Start page 095202-1
End page 095202-18
Total pages 18
Editor Alexander Its
Michio Jimbo
Jean-Michel Maillet
Place of publication College Park, MD, United States
Publisher American Institute of Physics
Language eng
Abstract We consider a superintegrable quantum potential in two-dimensional Euclidean space with a second and a third order integral of motion. The potential is written in terms of the fourth Painlevé transcendent. We construct for this system a cubic algebra of integrals of motion. The algebra is realized in terms of parafermionic operators and we present Fock-type representations which yield the corresponding energy spectra. We also discuss this potential from the point of view of higher order supersymmetric quantum mechanics and obtain ground state wave functions.
Keyword Physics, Mathematical
Physics
PHYSICS, MATHEMATICAL
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Article # 095202. Special issue: Integrable Quantum Systems and Solvable Statistical Mechanics Models.

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
ERA 2012 Admin Only
 
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Citation counts: TR Web of Science Citation Count  Cited 51 times in Thomson Reuters Web of Science Article | Citations
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Created: Mon, 24 Oct 2011, 23:42:51 EST by Ian Marquette on behalf of Mathematics