Supersymmetry, Shape Invariance and Solvability of $A_{N-1}$ and $BC_{N}$ Calogero-Sutherland Model

TL;DR

This paper employs supersymmetry and shape invariance techniques to re-derive the spectra of $A_{N-1}$ and $BC_N$ Calogero-Sutherland models, providing insights into their eigenfunctions and discussing extension challenges.

Contribution

It introduces a novel approach using supersymmetry and shape invariance to analyze Calogero-Sutherland models, offering a new perspective on their spectral properties.

Findings

Successfully re-derived spectra for $A_{N-1}$ and $BC_N$ models

Provided methods to obtain eigenfunctions

Discussed extension difficulties to trigonometric models

Abstract

Using the ideas of supersymmetry and shape invariance we re-derive the spectrum of the $A_{N-1}$ and $BC_N$ Calogero-Sutherland model. We briefly discuss as to how to obtain the corresponding eigenfunctions. We also discuss the difficulties involved in extending this approach to the trigonometric models.