Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials
arXiv:1609.05781 · doi:10.1016/j.aop.2017.03.019
Abstract
By using the technique of supersymmetric quantum mechanics, we study a quasi exactly solvable extension of the N-particle rational Calogero model with harmonic confining interaction. Such quasi exactly solvable many particle system, whose effective potential in the radial direction yields a supersymmetric partner of the radial harmonic oscillator, is constructed by including new long-range interactions to the rational Calogero model. An infinite number of bound state energy levels are obtained for this system under certain conditions. We also calculate the corresponding bound state wave functions in terms of the recently discovered exceptional orthogonal Laguerre polynomials.
10 pages, Latex, No figs, Version to appear in Annals of Physics
References in corpus (3)
Cited by in corpus (5)
- A class of exactly solvable rationally extended non-central potentials in Two and Three Dimensions
- A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
- Rationally extended many-body truncated Calogero-Sutherland model
- Supersymmetry and Shape Invariance of exceptional orthogonal polynomials
- Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry