Quantum & Classical Eigenfunctions in Calogero & Sutherland Systems

TL;DR

This paper provides an analytic proof that frequencies of small oscillations are quantized in Calogero and Sutherland systems, and presents explicit classical and quantum eigenfunctions for these integrable models based on root systems.

Contribution

It offers a rigorous proof of frequency quantization and explicit eigenfunctions for C-S systems using recent theoretical developments.

Findings

Proof of quantized oscillation frequencies

Explicit classical eigenfunctions for C-S systems

Explicit quantum eigenfunctions for C-S systems

Abstract

An interesting observation was reported by Corrigan-Sasaki that all the frequencies of small oscillations around equilibrium are " quantised" for Calogero and Sutherland (C-S) systems, typical integrable multi-particle dynamics. We present an analytic proof by applying recent results of Loris-Sasaki. Explicit forms of `classical' and quantum eigenfunctions are presented for C-S systems based on any root systems.