2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91762We review various unitary time-dependent perturbation theories and compare them formally and numerically. We show that the Kolmogorov-Arnold-Moser technique performs better owing to both the superexponential character of correction terms and the possibility to optimize the accuracy of a given level of approximation which is explored in details here. As an illustration, we consider a two-level system driven by short pulses beyond the sudden limit.15 pages, 5 color figuresQuantum Physicstext