QES extension of Calogero model associated with exceptional orthogonal polynomials

B. Basu-Mallick, Bhabani Prasad Mandal, Pinaki Roy

Published 2016-09-10Version 1

By using the technique of supersymmetric quantum mechanics, we study a quasi exactly solvable (QES) extension of the $N$-particle rational Calogero model with harmonic confining interaction. Such QES 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.