  We 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.
