Multi-Particle Quasi Exactly Solvable Difference Equations

TL;DR

This paper introduces multi-particle quasi-exactly solvable difference equations by deforming known integrable systems, providing explicit examples with finite exactly solvable eigenvalues and functions, extending previous single-particle results.

Contribution

It extends single-particle quasi-exactly solvable difference equations to multi-particle systems based on deformations of well-known integrable models.

Findings

Derived explicit multi-particle quasi-exactly solvable Hamiltonians

Identified finite sets of exactly solvable eigenvalues and eigenfunctions

Extended single-particle results to multi-particle systems

Abstract

Several explicit examples of multi-particle quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable multi-particle Hamiltonians, the Ruijsenaars-Schneider-van Diejen systems. These are difference analogues of the quasi exactly solvable multi-particle systems, the quantum Inozemtsev systems obtained by deforming the well-known exactly solvable Calogero-Sutherland systems. They have a finite number of exactly calculable eigenvalues and eigenfunctions. This paper is a multi-particle extension of the recent paper by one of the authors on deriving quasi exactly solvable difference equations of single degree of freedom.