Quantum & Classical Eigenfunctions in Calogero & Sutherland Systems
نویسنده
چکیده
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.
منابع مشابه
Calogero-sutherland-moser Systems, Ruijsenaars-schneider-van Diejen Systems and Orthogonal Polynomials
The equilibrium positions of the multi-particle classical Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials associated with the classical root systems are described by the classical orthogonal polynomials; the Hermite, Laguerre and Jacobi polynomials. The eigenfunctions of the corresponding single-particle quantum CSM systems are also expressed in terms of the same ...
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