2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/21285A relation between the number of bound collective excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalises Levinson's theorem. Specific features of the Bogoliubov model such as complex-energy and continuum bound states are discussed and a numerical example is given.4 pages, 3 figuresSoft Condensed Mattertext