2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100094In this paper we consider a general model of an atom with n energy levels interacting with n-1 external (laser) fields which is a natural extension in the two and three level systems. We exactly solve the Schr{\" o}dinger equation to obtain a Rabi oscillation when n = 4 and 5, which will constitute a quantum logic gate of Quantum Computation based on four and five level systems.Latex file ; 14 pages ; 1 figure ; many typos corrected. To appear in Yokohama Mathematical JournalQuantum PhysicsMathematical Physicstext