Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems

Marquette, Ian (2012) Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems. Journal of Mathematical Physics, 53 1: 012901.1-012901.12. doi:10.1063/1.3676075

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Author Marquette, Ian
Title Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
Publication date 2012-01-01
Sub-type Article (original research)
DOI 10.1063/1.3676075
Open Access Status File (Publisher version)
Volume 53
Issue 1
Start page 012901.1
End page 012901.12
Total pages 12
Place of publication College Park, MD, United States
Publisher American Institute of Physics
Collection year 2013
Language eng
Abstract We recall results concerning one-dimensional classical and quantum systems with ladder operators. We obtain the most general one-dimensional classical systems, respectively, with a third and a fourth-order ladder operators satisfying polynomial Heisenberg algebras. These systems are written in terms of the solutions of quartic and quintic equations. They are the classical equivalent of quantum systems involving the fourth and fifth Painlevé transcendents. We use these results to present two new families of superintegrable systems and examples of trajectories that are deformation of Lissajous's figures.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article # 012901

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 10 times in Thomson Reuters Web of Science Article | Citations
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Created: Sun, 26 Feb 2012, 16:00:29 EST by System User on behalf of Mathematics