text: This is the point at which the rotating wave approximation is made.  The dipole approximation has been assumed, and for this to remain valid the electric field must be near resonance with the atomic transition.  This means that  and the complex exponentials multiplying  and  can be considered to be rapidly oscillating.  Hence on any appreciable time scale, the oscillations will quickly average to 0.  The rotating wave approximation is thus the claim that these terms may be neglected and thus the Hamiltonian can be written in the interaction picture as
  Finally, transforming back into the Schrödinger picture, the Hamiltonian is given by
  Another criterion for rotating wave approximation is the weak coupling condition, that is, the Rabi frequency should be much less than the transition frequency.
  At this point the rotating wave approximation is complete.  A common first step beyond this is to remove the remaining time dependence in the Hamiltonian via another unitary transformation.