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
Subject 3109 Statistical and Nonlinear Physics
2610 Mathematical Physics
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.
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.
Keyword Physics, Mathematical
Physics
PHYSICS, MATHEMATICAL
Q-Index Code C1
Q-Index Status Confirmed Code
Grant ID DP110101414
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
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