Dynamical r-matrices and Separation of Variables: The Generalised Calogero-Moser Model

TL;DR

This paper extends the classical Calogero-Moser model by coupling it with the Gaudin model, uses a known dynamical r-matrix to separate variables, and then quantizes the model to solve the Schrödinger equation.

Contribution

It introduces a generalized Calogero-Moser model coupled with the Gaudin model and applies a specific dynamical r-matrix for variable separation in both classical and quantum frameworks.

Findings

Successful separation of variables in the classical generalized model.

Canonical quantization of the model achieved.

Application of the same r-matrix to solve the quantum Schrödinger equation.

Abstract

A generalisation of the classical Calogero-Moser model obtained by coupling it to the Gaudin model is considered. The recently found classical dynamical r-matrix [E. Billey, J. Avan and O. Babelon, PAR LPTHE 93-55] for the Euler-Calogero-Moser model is used to separate variables for this generalised Calogero-Moser model in the case in which there are two Calogero-Moser particles. The model is then canonically quantised and the same classical r-matrix is employed to separate variables in the Schr\"odinger equations.