# A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems

## TL;DR

This paper constructs exactly solvable rational extensions of Calogero-Wolfes 3-body problems, providing explicit energy spectra and eigenfunctions expressed via exceptional orthogonal polynomials, advancing the understanding of integrable quantum systems.

## Contribution

It introduces a new class of exactly solvable rationally extended 3-body potentials based on Calogero-Wolfes models, with solutions involving exceptional orthogonal polynomials.

## Key findings

- Derived explicit energy eigenvalues and eigenfunctions.
- Established the connection with exceptional orthogonal polynomials.
- Extended the class of solvable 3-body quantum models.

## Abstract

In this work, we start from the well known Calogero-Wolfes type 3-body problems on a line and construct the corresponding exactly solvable rationally extended 3-body potentials. In particular, we obtain the corresponding energy eigenvalues and eigenfunctions which are in terms of the product of Xm Laguerre and Xp Jacobi exceptional orthogonal polynomials where both m,p = 1,2,3,....