Abstract: An introduction is presented to a recently established nonperturbative approach to the transitions between atomic states induced by weak electromagnetic waves. A special case of the general solution is calculated and discussed in detail. Results of the nonperturbative approach reduce under perturbation condition to those obtained by the time- dependent perturbative method, but overcome the difficulty that the perturbative results are obviously unreasonable in the near resonant region. According to the nonperturbative solution, the electric-dipole selection rules are approximately recovered for short time. For large time, however, probabilities for forbidden transitions may become comparable with those for allowed ones.

Key words: induced transition, nonperturbative approach, rotating-wave approximation, electromagnetic interaction