Exact solutions of an elliptic Calogero--Sutherland model

TL;DR

This paper provides algebraic solutions for an elliptic Calogero--Sutherland model, explicitly solving for ground and excited states in the quantum case for two particles, advancing understanding of integrable systems with elliptic interactions.

Contribution

It introduces a totally algebraic method to partially solve the quantum elliptic Calogero--Sutherland model, including explicit solutions for two particles.

Findings

Explicit ground state for N=2

Lowest excitations calculated for N=2

Partial algebraic solutions for the quantum model

Abstract

A model describing N particles on a line interacting pairwise via an elliptic function potential in the presence of an external field is partially solved in the quantum case in a totally algebraic way. As an example, the ground state and the lowest excitations are calculated explicitly for N=2.