New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

Journal Article · Mon Apr 15 00:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4798807· OSTI ID:22162867

Marquette, Ian ^[1]; Quesne, Christiane ^[2]

---

1. School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072 (Australia)
2. Physique Nucleaire Theorique et Physique Mathematique, Universite Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)

In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this paper, we construct from Hermite and Laguerre EOP and their related quantum systems new 2D superintegrable Hamiltonians with higher-order integrals of motion and the polynomial algebras generated by their integrals of motion. We obtain the finite-dimensional unitary representations of the polynomial algebras and the corresponding energy spectrum. We also point out a new type of degeneracies of the energy levels of these systems that is associated with holes in sequences of EOP.

• OSTI ID: 22162867
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 4; Other Information: (c) 2013 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENERGY LEVELS
ENERGY SPECTRA
EXACT SOLUTIONS
HAMILTONIANS
POLYNOMIALS