A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero-Moser Hamiltonians

TL;DR

This paper introduces a recursive method to construct symmetric joint eigenfunctions for hyperbolic Calogero-Moser Hamiltonians, linking them to hypergeometric functions and providing integral representations.

Contribution

It presents a novel recursive scheme for eigenfunction construction, connecting integrable systems with special functions and offering explicit integral formulas.

Findings

Eigenfunctions constructed via recursion scheme

Integral representations involve elementary functions

Connection established with Heckman-Opdam hypergeometric functions

Abstract

We obtain symmetric joint eigenfunctions for the commuting PDOs associated to the hyperbolic Calogero-Moser N-particle system. The eigenfunctions are constructed via a recursion scheme, which leads to representations by multidimensional integrals whose integrands are elementary functions. We also tie in these eigenfunctions with the Heckman-Opdam hypergeometric function for the root system A_{N-1}.