Connection between Calogero-Marchioro-Wolfes type few-body models and free oscillators

TL;DR

This paper demonstrates a precise link between Calogero-Marchioro-Wolfes type few-body models and free oscillators, providing a method to find new solvable quantum models and proving their integrability.

Contribution

It establishes an exact correspondence between these complex models and free oscillators, enabling the derivation of eigenstates and integrability proof.

Findings

Eigenstates of the models are explicitly constructed.

Quantum integrability of the models is proven.

Method for discovering new solvable models is demonstrated.

Abstract

We establish the exact correspondence of the Calogero-Marchioro-Wolfes model and several of its generalizations with free oscillators. This connection yields the eigenstates and leads to a proof of the quantum integrability. The usefulness of our method for finding new solvable models is then demonstrated by an example.