Explicit formulas for the eigenfunctions of the N-body Calogero model

TL;DR

This paper presents explicit formulas for eigenfunctions of the N-body Calogero model, a quantum system with inverse-square interactions, using a novel solution algorithm applicable to various root systems.

Contribution

The authors develop a new algorithm that provides explicit eigenfunctions for the Calogero model for any particle number and coupling, extending to classical root system variants.

Findings

Explicit eigenfunctions derived for arbitrary N and coupling

Algorithm applicable to all classical root system Calogero models

Enhanced understanding of the model's spectral properties

Abstract

We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the inter-particle distance. We elaborate a novel solution algorithm which allows us to obtain fully explicit formulas for its eigenfunctions, for arbitrary coupling parameter and particle number. We also show that our method applies, with minor changes, to all Calogero models associated with classical root systems.