We now assume that the resonance frequency of the cavity is near the transition frequency of the atom, that is, we assume formula_91. Under this condition, the exponential terms oscillating at formula_92 are nearly resonant, while the other exponential terms oscillating at formula_93 are nearly anti-resonant. In the time formula_94 that it takes for the resonant terms to complete one full oscillation, the anti-resonant terms will complete many full cycles. Since over each full cycle formula_95 of anti-resonant oscillation, the effect of the anti-resonant terms is 0, the net effect of the quickly oscillating anti-resonant terms tends to average to 0 for the timescales over which we wish to analyze resonant behavior. We may thus neglect the anti-resonant terms altogether, since their value is negligible compared to that of the nearly resonant terms. This approximation is known as the rotating wave approximation, and it accords with the intuition that energy must be conserved. Then the interaction Hamiltonian (taking formula_96 to be real for simplicity) is: