Eigenfunctions for SU(N) particles with 1/r^2 interaction in harmonic confinement

Abstract

We find a set of the 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 wave function 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.