Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

Hoque, Md. Fazlul, Marquette, Ian, Post, Sarah and Zhang, Yao-Zhong (2018) Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials. Annals of Physics, 391 203-215. doi:10.1016/j.aop.2018.02.008

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Author Hoque, Md. Fazlul
Marquette, Ian
Post, Sarah
Zhang, Yao-Zhong
Title Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
Journal name Annals of Physics   Check publisher's open access policy
ISSN 1096-035X
0003-4916
Publication date 2018-02-19
Year available 2018
Sub-type Article (original research)
DOI 10.1016/j.aop.2018.02.008
Open Access Status File (Author Post-print)
Volume 391
Start page 203
End page 215
Total pages 13
Place of publication Maryland Heights, MO United States
Publisher Academic Press
Language eng
Subject 3100 Physics and Astronomy
Abstract We introduce an extended Kepler–Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.
Keyword Deformed oscillator algebras
Exceptional orthogonal polynomials
Ladder operator
Polynomial algebras
Superintegrability
Q-Index Code C1
Q-Index Status Provisional Code
Grant ID 11775177
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Fri, 16 Mar 2018, 00:34:25 EST