Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials

TL;DR

This paper introduces a new quasi exactly solvable extension of the Calogero model using supersymmetric quantum mechanics, incorporating exceptional orthogonal polynomials to find bound states.

Contribution

It presents a novel many-particle system with extended interactions, solvable for an infinite number of bound states, linked to exceptional orthogonal Laguerre polynomials.

Findings

Infinite bound state energy levels obtained

Bound state wave functions expressed with exceptional Laguerre polynomials

Extended Calogero model with supersymmetric partner potential

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.