A new integro-differential operator equation which describes the propagation of a quantized radiation field in a resonant medium is obtained. We have investigated a system of atoms on the basis of the interaction of H-like atoms through the field of virtual photons, taking into account electronic and positronic intermediate states in the atomic spectrum. This interaction is treated as a third-order effect in quantum electrodynamics. We suggest a new method to solve boundary-value problems in quantum optics which employs the joint system of material and field equations.