2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/92055We review the quantum adiabatic approximation for closed systems, and its recently introduced generalization to open systems (M.S. Sarandy and D.A. Lidar, e-print quant-ph/0404147). We also critically examine a recent argument claiming that there is an inconsistency in the adiabatic theorem for closed quantum systems [K.P. Marzlin and B.C. Sanders, Phys. Rev. Lett. 93, 160408 (2004)] and point out how an incorrect manipulation of the adiabatic theorem may lead one to obtain such an inconsistent result.v3: 11 pages, no figures. Published version. This pedagogical work is part comment on, part simplification of the paper "Inconsistency in the application of the adiabatic theorem" by K.-P. Marzlin and B.C. Sanders, Phys. Rev. Lett. 93, 160408 (2004)Quantum Physicstext