On the solution to the separated equation in the 3-particle Calogero-Moser problem

TL;DR

This paper presents an exact solution to the separated equation in the three-particle quantum Calogero-Moser problem with elliptic potential, specifically for integer coupling constants greater than one, aiding in solving the full problem.

Contribution

It provides the first explicit solution to the separated equation for special coupling constants in the three-particle Calogero-Moser problem with elliptic potential.

Findings

Solution valid for integer g > 1

Facilitates solving the three-particle CM problem

Applicable under certain boundary conditions

Abstract

We propose the exact solution of the equation in separated variable which appears in the process of constructing solutions to the quantum Calogero-Moser three-particle problem with elliptic two-particle potential $g(g-1)\wp(q)$. This solution is found for special values of coupling constants $g\in {\mathbb Z}, \, g>1$. It can be used for solving three-paricle CM problem under appropriate boundary conditions.