An explicit solution of the (quantum) elliptic Calogero-Sutherland model

TL;DR

This paper provides explicit formulas for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland model, extending the understanding of this integrable quantum system with a novel elliptic deformation of Jack polynomials.

Contribution

It introduces a formal power series solution for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland model for any coupling and particle number, including an elliptic deformation of Jack polynomials.

Findings

Explicit formulas for eigenvalues and eigenfunctions as power series.

General solution valid for arbitrary coupling and particle number.

Elliptic deformation of Jack polynomials described.

Abstract

We present explicit formulas for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland (eCS) model as formal power series to all orders in the nome of the elliptic functions, for arbitrary values of the (positive) coupling constant and particle number. Our solution gives explicit formulas for an elliptic deformation of the Jack polynomials.