Explicit Solution of the (Quantum) Elliptic Calogero-Sutherland Model.

The elliptic Calogero-Sutherland model is a quantum many body system of identical particles moving on a circle and interacting via two body potentials proportional to the Weierstrass $${\wp}$$-function. It also provides a natural many-variable generalization of the Lamé equation. Explicit formulas for the eigenfunctions and eigenvalues of this model as infinite series are obtained, to all orders and for arbitrary particle numbers and coupling parameters. These eigenfunctions are an elliptic deformation of the Jack polynomials. The absolute convergence of these series is proved in special cases, including the two-particle (=Lamé) case for non-integer coupling parameters and sufficiently small elliptic deformation. [ABSTRACT FROM AUTHOR]