An explicit solution of the (quantum) elliptic Calogero-Sutherland model

Edwin Langmann

Published 2004-07-21, updated 2004-09-06Version 3

We present explicit formulas for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland (eCS) model as formal power series to all orders in the nome of the elliptic functions, for arbitrary values of the (positive) coupling constant and particle number. Our solution gives explicit formulas for an elliptic deformation of the Jack polynomials.