On an Explicit Set of Complete Eigenfunctions for the Calogero-Sutherland Model

TL;DR

This paper introduces an operator method to explicitly generate a complete set of eigenfunctions for the Calogero-Sutherland model, clarifying their relation to the model's general eigenfunctions and their focus on center of mass motion.

Contribution

It provides a new operator-based approach to explicitly construct eigenfunctions for the Calogero-Sutherland model, linking them to the model's overall eigenfunctions and highlighting their physical interpretation.

Findings

Explicit eigenfunctions describe only center of mass motion

Connection established between basis set and general eigenfunctions

Method offers a systematic way to generate eigenfunctions

Abstract

An operator method is provided to generate an explicit set of complete eigenfunctions for the Calogero-Sutherland model, obtained earlier by Vacek, Okiji and Kawakami, through a special ansatz. We find the connection of the above basis set with the general eigenfunctions of this model and explicitly show that these states describe {\it only} the center of mass motion.