Abstract: We study the exact solutions of a particular class of N confined particles of equal mass, with N = 3^k (k = 2, 3,...), in the D = 1 dimensional space. The particles are clustered in clusters of three particles. The interactions involve a confining mean field, two-body Calogero type of potentials inside the cluster, interactions between the centres of mass of the clusters and finally a non-translationally invariant Nbody potential. The case of nine particles is exactly solved, in a first step, by providing the full eigensolutions and eigenenergies. Extending this procedure, the general case of N particles (N = 3^k, k ≥ 2) is studied in a second step. The exact solutions are obtained via appropriate coordinate transformations and separation of variables. The eigenwave functions and the corresponding energy spectrum are provided.
N° Revue: Few-Body Systems, Volume 57, Numéro 9, Springer Vienna - Pagination: pp 773–7 - Date: 01/09/2016
URL: DOI: 10.1007/s00601-016-1107-z
Mots cles: N - particules, Clusters, Three particles, Non-translationally invariant N-body potential, coordinate transformations, eparation of variables, eigenwave functions, energy spectrum, Schrôdinger equation
co_auteurs: M Lassaut