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

TL;DR

This paper derives explicit solutions for generalized Calogero-Sutherland models associated with the classical groups BC_N and C_N using a collective field approach, extending known solutions from the A_{N-1} case.

Contribution

It introduces a systematic method to construct wave functions and compute energy eigenvalues for BC_N and C_N models based on the A_{N-1} solutions.

Findings

Explicit wave functions for BC_N and C_N models obtained.

Energy eigenvalues derived for these models.

A unified method connecting different group types.

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.