2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129832In this paper we present an invariant perturbation theory to adiabatic process according to the concepts of adiabatic orbits, adiabatic evolution orbit and U(1)-invariant adiabatic orbit. The probabilities of keeping the adiabatic orbit in the first-order and the second-order approximation are calculated, respectively. We also give a convenient sufficient condition.4 pages, no figuresQuantum Physicstext