2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184308An 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 addedHigh Energy Physics - TheoryCondensed MatterMathematical PhysicsExactly Solvable and Integrable SystemsQuantum Physicstext