Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion

Marquette, Ian (2009) Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion. Journal of Mathematical Physics, 50 12: 122102-1-122102-10. doi:10.1063/1.3272003

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Author Marquette, Ian
Title Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
1527-2427
Publication date 2009-12-01
Year available 2009
Sub-type Article (original research)
DOI 10.1063/1.3272003
Open Access Status File (Publisher version)
Volume 50
Issue 12
Start page 122102-1
End page 122102-10
Total pages 10
Place of publication College Park, MD, United States
Publisher American Institute of Physics
Language eng
Abstract The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral and apply Mielnik’s construction in supersymmetric quantum mechanics. We obtain a new superintegrable potential separable in Cartesian coordinates with a quadratic and quintic integrals and also one with a quadratic integral and an integral of order of 7. We also construct a superintegrable system written in terms of the fourth Painlevé transcendent with a quadratic integral and an integral of order of 7.
Keyword Physics, Mathematical
Physics
PHYSICS, MATHEMATICAL
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Article # 122102

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 27 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 30 times in Scopus Article | Citations
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Created: Mon, 24 Oct 2011, 23:45:36 EST by Ian Marquette on behalf of Mathematics