Rationally extended many-body truncated Calogero-Sutherland model

TL;DR

This paper develops a rational extension of the truncated Calogero-Sutherland model, providing exact solutions with modified eigenfunctions expressed via exceptional orthogonal polynomials, and generalizes it to an Xm case.

Contribution

It introduces a novel rational extension of the truncated Calogero-Sutherland model with exact solutions and extends it to a more general Xm case, unifying several models.

Findings

Eigenvalues remain unchanged in the extended model.

Eigenfunctions are expressed in terms of exceptional X1 Laguerre polynomials.

The model reduces to known models in specific limits.

Abstract

We construct a rational extension of the truncated Calogero-Sutherland model by Pittman et al. The exact solution of this rationally extended model is obtained analytically and it is shown that while the energy eigenvalues remain unchanged, however the eigenfunctions are completely different and written in terms of exceptional X1 Laguerre orthogonal polynomials. The rational model is further extended to a more general, the Xm case by introducing m dependent interaction term. As expected, in the special case of m = 0, the extended model reduces to the conventional model of Pittman et al. In the two appropriate limits, we thereby obtain rational extensions of the celebrated Calogero-Sutherland as well as Jain-Khare models.