A model of the Calogero type in the D-dimensional space

PTHIn a previous paper, we have proposed a new integrable Hamiltonian describing two interacting particles in a harmonic mean field in D = 1 dimensional space. Here, we generalize this Hamiltonian to the D ≥ 2 dimensional space. We show that the system is exactly solvable for a certain domain of the interaction constant, and that the size of this domain increases with D. We also show this D-dimensional Hamiltonian to be supersymmetric and shape invariant, very much as in the D = 1 case