2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/93970We perform the exact numerical diagonalization of the Hamiltonians that describe both degenerate and nondegenerate parametric amplifiers, by exploiting the conservation laws pertaining each device. We clarify the conditions under which the parametric approximation holds, showing that the most relevant requirement is the coherence of the pump after the interaction, rather than its undepletion.19 pages, 9figs, LaTeX with cimento.cls documentclass (included). To appear on Nuovo Cimento BQuantum Physicstext