Equivalence of the Calogero-Sutherland model to free harmonic oscillators

A similarity transformation is constructed, through which a system of parti cles interacting with inverse-square two-body and harmonic potentials in on e dimension can be mapped identically to a set of free harmonic oscillators . This equivalence provides a straightforward method to find the complete s et of eigenfunctions, the exact constants of motion, and a linens W1+infini ty algebra associated with this model. It is also demonstrated that a large class of models with long-range interactions, both in one and higher dimen sions can be made equivalent to decoupled oscillators. [S0163-1829(99)51404 -5].