Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators

Details Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators

1997-10-03

arxiv.org/abs/cond-mat/9710035v3

Phys.Rev. B59 (1999) R2490-R2493

Physics

Condensed Matter

9 pages, REVTeX, Completely revised, few new equations and references are added

Scientific paper

10.1103/PhysRevB.59.R2490

A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This equivalence provides a straightforward method to find the complete set of eigenfunctions, the exact constants of motion and a linear $W_{1+\infty}$ algebra associated with this model. It is also demonstrated that a large class of models with long-range interactions, both in one and higher dimensions can be made equivalent to decoupled oscillators.

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