Generalization of the spectroscopic correspondence principle on time dependence of quantum transitions

In this work, we generalize the well-known spectroscopic correspondence principle on time dependence of quantum transitions by comparing the time dependence of the energy of an electromagnetic pulse absorbed by the two-level system and classical linear oscillator. Formulas for the above-mentioned dependences are derived for two cases, viz. systems with and without relaxation. It is shown that in the first case the results for quantum and classical systems coincide exactly. If the relaxation is sufficiently large, there is a noticeable difference between two time dependences of absorbed energy.