Families of 2D superintegrable anisotropic Dunkl oscillators and algebraic derivation of their spectrum

Isaac, Phillip S. and Marquette, Ian (2016) Families of 2D superintegrable anisotropic Dunkl oscillators and algebraic derivation of their spectrum. Journal of Physics A: Mathematical and Theoretical, 49 11: 1-13. doi:10.1088/1751-8113/49/11/115201


Author Isaac, Phillip S.
Marquette, Ian
Title Families of 2D superintegrable anisotropic Dunkl oscillators and algebraic derivation of their spectrum
Journal name Journal of Physics A: Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8121
1751-8113
Publication date 2016-02-02
Year available 2016
Sub-type Article (original research)
DOI 10.1088/1751-8113/49/11/115201
Open Access Status Not Open Access
Volume 49
Issue 11
Start page 1
End page 13
Total pages 13
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2017
Language eng
Formatted abstract
We generalize the construction of integrals of motion for quantum superintegrable models and the deformed oscillator algebra approach. This is presented in the context of 1D systems admitting ladder operators satisfying a parabosonic algebra involving reflection operators and more generally clambda extended oscillator algebras with grading. We apply the construction on two-dimensional clambda oscillators. We also introduce two new superintegrable Hamiltonians that are the anisotropic Dunkl and the singular Dunkl oscillators. Integrals are constructed by extending the approach of Daskaloyannis to include grading. An algebraic derivation of the energy spectra of the two models is presented, making use of finite dimensional unitary representations. We show how the spectra divide into sectors, and make comparisons with the physical case.
Keyword Superintegrable systems
Polynomial algebras
Deformed oscillator
Dunkl oscillator
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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