In Chapter 7 of C. J. Foot's Atomic Physics, Foot discusses the interaction of a two-level atom with radiation. He derives the phenomenon of Rabi flopping from the Schrodinger equation, using perturbation theory and the rotating wave approximation as is standard to do. Then he says this:
The population oscillates between the two levels. When $Ωt = π$ all the population has gone from level 1 into the upper state, $|c_2(t)|^2 = 1$, and when $Ωt = 2π$ the atom has returned to the lower state. This behaviour is completely different from that of a two-level system governed by rate equations where the populations tend to become equal as the excitation rate increases and population inversion cannot occur.
What is the distinction he draws here? How does one reconcile the fact that the use of rate equations generally does not allow for population inversion between the two levels, as he says, but that the Schrodinger equation does? Is there a more subtle issue, such as the assumption of coherence in the case of Rabi flopping, involved here? Is it just that the "rate equation" model is simply wrong?
I'm happy to try to clarify the question if it needs it.