SU(m|n) Supersymmetric Calogero–Sutherland Model Confined in Harmonic Potential

Abstract

In this work, we study a continuous quantum system of a mixture of bosons and fermions with the supersymmetry SU (m|n). The particles are confined in a harmonic well and interact with each other through the 1/r2 interaction. An eigenstate of the Hamiltonian is constructed explicitly for the most general SU (m|n) case and its energy is given explicitly. It is argued that this eigenstate is the ground state of the system. Moreover, we construct some excited states giving an equally spaced spectrum. In the limiting case where there are no bosons in the system, our results reduce to those obtained previously.