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. Further, 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.

23 pages, RevTeX, no figure, some clarifications added, version to appear in Journal of Physics A

References in corpus (2)

• Hidden Algebras of the (super) Calogero and Sutherland models
• Exactly Solvable Models in Arbitrary Dimensions

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• Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
• Dynamical symmetries of the Calogero-Coulomb model