Relationship Between the Energy Eigenstates of Calogero-Sutherland Models With Oscillator and Coulomb-like Potentials

Details Relationship Between the Energy Eigenstates of Calogero-Sutherland Models With Oscillator and Coulomb-like Potentials Relationship Between the Energy Eigenstates of Calogero-Sutherland Models With Oscillator and Coulomb-like Potentials

1998-08-13

arxiv.org/abs/solv-int/9808005v2

Journal of Physics A : Math. & Gen. 32 (1999) 2129-2140

Physics

Condensed Matter

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

Scientific paper

10.1088/0305-4470/32/11/008

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.

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