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 Δ Δ ω ω ≪ ≪ ω ω L + ω ω 0 and the complex exponentials multiplying Ω Ω ~ ~ and Ω Ω ~ ~ ∗ ∗ 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