Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators

Abstract

A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This equivalence provides a straightforward method to find the complete set of eigenfunctions, the exact constants of motion and a linear $W_{1+\infty }$ algebra associated with this model. It is also demonstrated that a large class of models with long-range interactions, both in one and higher dimensions can be made equivalent to decoupled oscillators.

9 pages, REVTeX, Completely revised, few new equations and references are added

References in corpus (1)

• Orthogonal Symmetric Polynomials Associated with the Calogero Model

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