Exclusion Statistics Interpretation of the Quantum Calogero Model

Abstract

Following the definition of Haldane's exclusion statistics, we proposea new and simple representation of the spectrum and the state countingof the quantum Calogero model. We show that N non-interactingparticles with statistical interactions confined in an externalharmonic well give exactly the same energy spectrum and the samedegeneracy as those of the N-particle quantum Calogero model. We alsoshow that this picture exactly corresponds to the generalized idealgas, which was introduced by Bernard and Wu.