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

TL;DR

This paper derives exact eigenfunctions and energy spectra for an SU(N) Calogero-Sutherland model with harmonic confinement, incorporating spin degrees of freedom for bosons and fermions, using explicit wave function construction.

Contribution

It provides explicit construction of eigenfunctions and energy spectra for the SU(N) Calogero-Sutherland model with harmonic confinement, including spin degrees of freedom.

Findings

Explicit eigenfunctions combining Jastrow and Hermite polynomials

Exact energy spectrum as sum of ground and excited states

Applicable to both bosonic and fermionic particles with SU(ν) symmetry

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.