Quantum and classical eigenfunctions in Calogero and Sutherland systems

Abstract

An interesting observation was reported by Corrigan–Sasaki that all the frequencies of small oscillations around equilibrium are 'quantized' for Calogero and Sutherland (CS) 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 CS systems based on any root system.