Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

Journal Article · Sun Apr 15 04:00:00 EDT 2018 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2018.02.008· OSTI ID:22848314

Marquette, Ian ^[1]; Post, Sarah ^[2]; Zhang, Yao-Zhong ^[1]

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1. School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia)
2. Department of Mathematics, University of Hawaii at Manoa, Honolulu, HI 96822 (United States)

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.

• OSTI ID: 22848314
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 391; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
COORDINATES
ENERGY SPECTRA
HAMILTONIANS
OSCILLATORS
POLYNOMIALS
QUANTUM SYSTEMS
RECURSION RELATIONS
SIMULATION
SPHERICAL CONFIGURATION
STRUCTURE FUNCTIONS
WAVE FUNCTIONS