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.

11 pages, latex, no figures. A subtitle is added. Comments on additional solutions for B_N and D_N cases, and some additional references are included. Version to appear in Nuclear Physics B

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• Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
• Correlation functions of the BC Calogero-Sutherland model
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• All the Exact Solutions of Generalized Calogero-Sutherland Models