New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems

Marquette, Ian and Quesne, Christiane (2013) New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems. Journal of Mathematical Physics, 54 10: 102102-1-102102-12. doi:10.1063/1.4823771

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Author Marquette, Ian
Quesne, Christiane
Title New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
Publication date 2013-10-01
Year available 2013
Sub-type Article (original research)
DOI 10.1063/1.4823771
Open Access Status File (Author Post-print)
Volume 54
Issue 10
Start page 102102-1
End page 102102-12
Total pages 12
Place of publication College Park, United States
Publisher American Institute of Physics
Language eng
Formatted abstract
New ladder operators are constructed for a rational extension of the harmonic oscillator associated with type III Hermite exceptional orthogonal polynomials and characterized by an even integer m. The eigenstates of the Hamiltonian separate into m + 1 infinite-dimensional unitary irreducible representations of the corresponding polynomial Heisenberg algebra. These ladder operators are used to construct a higher-order integral of motion for two superintegrable two-dimensional systems separable in cartesian coordinates. The polynomial algebras of such systems provide for the first time an algebraic derivation of the whole spectrum through their finite-dimensional unitary irreducible representations.
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 13 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 12 times in Scopus Article | Citations
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Created: Fri, 29 Nov 2013, 07:15:31 EST by System User on behalf of School of Mathematics & Physics