Exact solutions of generalized Calogero-Sutherland models: BCN and CN 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 the 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.