Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
- School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia)
- 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, Vol. 391; Other Information: © 2018 Elsevier Inc. All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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