2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135269An essentially-exact approach to compute the wavefunction in the time-dependent many-boson Schrödinger equation is derived and employed to study accurately the process of splitting a trapped condensate when ramping-up a barrier such that a double-well is formed. We follow the role played by many-body excited states during the splitting process. Among others, a 'counter-intuitive' regime is found in which the evolution of the condensate when the barrier is ramped-up sufficiently slow {\it is not} to the ground-state which is a fragmented condensate, but to a low-lying excited-state which is a coherent condensate. Experimental implications are discussed.11 pages, 3 figuresOther Condensed Mattertext