New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

Marquette, Ian and Quesne, Christiane (2013) New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials. Journal of Mathematical Physics, 54 4: 042102-1-042102-16. doi:10.1063/1.4798807

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Author Marquette, Ian
Quesne, Christiane
Title New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
1527-2427
Publication date 2013-04
Sub-type Article (original research)
DOI 10.1063/1.4798807
Open Access Status File (Publisher version)
Volume 54
Issue 4
Start page 042102-1
End page 042102-16
Total pages 16
Place of publication United States
Publisher American Institute of Physics
Collection year 2014
Language eng
Formatted abstract
In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this paper, we construct from Hermite and Laguerre EOP and their related quantum systems new 2D superintegrable Hamiltonians with higher-order integrals of motion and the polynomial algebras generated by their integrals of motion. We obtain the finite-dimensional unitary representations of the polynomial algebras and the corresponding energy spectrum. We also point out a new type of degeneracies of the energy levels of these systems that is associated with holes in sequences of EOP.
Keyword Conformally flat spaces
Supersymmetric quantum-mechanics
Classical structure-theory
Higher-order SUSY
Heisenberg algebras
3rd-order integrals
Stackel transform
Potentials
Classification
Oscillator
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 18 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 17 times in Scopus Article | Citations
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