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Journal of Physics A Mathematical and General

Integral representation for the eigenstates of the spin system with inverse square interactions

Kazuhiro Hikami

Published Aug 7, 1994• 9 citations
Publisher

Abstract

We consider the Calogero-Sutherland-Moser system with spin - 1/2 . We give the integral representation for the ground state wavefunction. Excited states of the Calogero spin model confined in the harmonic potential are also given.
DOI
10.1088/0305-4470/27/15/002

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We find a set of exact eigenfunctions which provide the energy spectrum for the quantum N-body Calogero-Sutherland model for fermions or bosons with SU( nu ) spin degrees of freedom moving in a harmonic confinement potential. The eigenfunctions are explicitly constructed as a simple product of the Jastrow wavefunction for the ground state and the Hermite polynomials introduced to generate the excited states. The corresponding energy spectrum is given by a sum of the correlated ground-state energy and of the excited-state energy for SU( nu ) free particles in a harmonic well.