Relationship between the energy eigenstates of Calogero-Sutherland models with oscillator and coulomb-like potentials

Abstract

We establish a simple algebraic relationship between the energy eigenstates of the rational Calogero-Sutherland model with harmonic oscillator and coulomb-like potentials. We show that there is an underlying SU(1,1) algebra in both of these models which plays a crucial role in such an identification. Furthermore, we show that our analysis is in fact valid for any many-particle system in arbitrary dimensions whose potential term (apart from the oscillator or the coulomb-like potential) is a homogeneous function of coordinates of degree -2. The explicit coordinate transformation which maps the coulomb-like problem to the oscillator one has also been determined in some specific cases.