Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials

Marquette, Ian (2009) Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials. Journal of Mathematical Physics, 50 1: 012101-1-012101-23. doi:10.1063/1.3013804

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Author Marquette, Ian
Title Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
1527-2427
Publication date 2009-01
Sub-type Article (original research)
DOI 10.1063/1.3013804
Open Access Status File (Publisher version)
Volume 50
Issue 1
Start page 012101-1
End page 012101-23
Total pages 23
Place of publication College Park, MD, United States
Publisher American Institute of Physics
Language eng
Formatted abstract
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integrals of motion. We construct the most general cubic algebra and we present specific realizations. We use them to calculate the energy spectrum. All classical and quantum superintegrable potentials separable in Cartesian coordinates with a third order integral are known. The general formalism is applied to quantum reducible and irreducible rational potentials separable in Cartesian coordinates in E2. We also discuss these potentials from the point of view of supersymmetric and PT-symmetric quantum mechanics.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Article # 012101

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 39 times in Thomson Reuters Web of Science Article | Citations
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Created: Mon, 24 Oct 2011, 13:39:23 EST by Ian Marquette on behalf of Mathematics