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

We establish a simple algebraic relationship between the energy eigenstates of the rational Calogero-Sutherland model with harmonic oscillator and cou lomb-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 identificatio n. Furthermore, we show that our analysis is in fact valid for any many-par ticle system in arbitrary dimensions whose potential term (apart from the o scillator or the coulomb-like potential) is a homogeneous function of coord inates 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.