[en] In a recent work, Abdel-Aty and Obada (2002 J. Phys. B: At. Mol. Opt. Phys. 35 807-13) analysed the quantum inversion of cold atoms in a microcavity, the motion of the atoms being described quantum mechanically. Two-level atoms were assumed to interact with a single mode of the cavity, and the off-resonance case was considered (namely the atomic transition frequency is detuned from the single-mode cavity frequency). We demonstrate in this paper that this case is incorrectly treated by these authors, and we therefore question their conclusions.