[en] It is presented the general and rigorous equation of motion for the reduced density matrix (RDM) describing the time evolution of a system A coupled to a system B for any initial statistical state. The corresponding perturbation expansion up to the second order in the interaction is derived and discussed for a variety of physical initial conditions. The formalism is applied to the interaction of radiation with matter in terms of a single-mode field coupled to a two-level atomic system through electric-dipole interaction. The equations of motion are solved for the dynamical variables describing the atomic system interacting with i) thermal and ii) coherent incident radiation or coupled to iii) a field produced by classical currents. It is shown that the ''effective'' semi-classical Hamiltonian can be established in the case ii), whereas the semi-classical approximation (SCA) is meaningless in the case i). The range of validity of the SCA is discussed in terms of the exactly solvable rotating-wave version of the dipole coupling. Drastic deviation from the SCA results are reported even in the limit of high intensity of the incident coherent field unless the coupling is very weak or the interaction time elapsed is very short. The relevance of the initial photon statistics is analyzed by comparing the SCA with the exact RDM. The validity of the SCA for various spectroscopic techniques is discussed