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Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators

N. Gurappa·Prasanta. K. Panigrahi
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Abstract

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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N. Gurappa, Prasanta. K. Panigrahi. 1997-12-10. Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators. https://doi.org/10.1103/physrevb.59.r2490

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