2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/49794This paper presents the operator form of the effective potential V governing the time evolution in 2 and 3 and n dimensional subspace of states. The general formula for the n dimensional case is considered the starting point for the calculation of the explicit formulae for 2 and 3 dimensional degenerate and non-degenerate cases. We relate the 2 and 3 dimensional cases to some physical systems which are currently investigated.17 pages. To appear in Acta Physica Polonica BHigh Energy Physics - Theorytext