N-fermion ground state of Calogero-Sutherland type models in two and higher dimensions

Abstract

I obtain the exact ground state of N fermions in D dimensions (D ≥ 2) in the case that the N particles are interacting via long-ranged two-body and three-body interactions and further they are also interacting via the harmonic oscillator potential. I also obtain the N-fermion ground state in the case that the oscillator potential is replaced by an N-body Coulomb-like interaction.