On the solution of the Calogero model and its generalization to the case of distinguishable particles

TL;DR

This paper solves the 3-body Calogero problem for arbitrary exchange statistics and numerically explores the 4-body spectrum, revealing new features and deviations from traditional models like Bethe ansatz and Haldane's statistics.

Contribution

It provides an exact solution for the 3-body Calogero model with arbitrary statistics and extends understanding through numerical analysis of the 4-body spectrum.

Findings

Energies are not linear with the interaction parameter .

Bethe ansatz and Haldane's statistics are not verified.

New spectral features differ from standard bosonic and fermionic cases.

Abstract

The 3-body Calogero problem is solved by separation of variables for arbitrary exchange statistics. A numerical computation of the 4-body spectrum is also presented. The results display new features in comparison with the standard case of bosons and fermions, for instance the energies are not linear with the interaction parameter $\nu$ and Bethe ansatz as well as Haldane's statistics are not verified.