Exact Solutions of Generalized Calogero-Sutherland Models -- BC_N and C_N cases

Abstract

Using a collective field method, we obtain explicit solutions of the generalized Calogero-Sutherland models that are characterized by the roots of the classical groups $B_N$ and $C_N$. Starting from the explicit wave functions for $A_{N-1}$ type expressed in terms of the singular vectors of the $W_N$ algebra, we give a systematic method to construct wave functions and derive energy eigenvalues for other types of theories.