Quantum & Classical Eigenfunctions in Calogero & Sutherland 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.

LaTeX2e 37 pages, references added, typo corrected, a few paragraphs added

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