Abstract: In 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.
N° Revue: Journal of Physics A: Mathematical and Theoretical, Journal of Physics A: Mathematical and Theoreti - Pagination: 8791-880 - Date: 12/07/2007
URL: http://iopscience.iop.org/article/10.1088/1751-8113/40/30/012/meta
Mots cles: Integrable Hamiltonian, Calogero model, D-dimensional space, Exactly solvable, Supersymmetry, Shape invariance
co_auteurs: M Lassaut, R J Lombard