Nonadiabatic transitions in a three-level system subjected to a laser radiation field with a smoothly varying frequency

Explicit expressions are obtained for the probabilities of transitions in a three-level system subjected to twofrequency laser radiation. The radiation or transition frequencies vary smoothly with time, passing through a resonance. The results obtained generalize the Landau–Zener solution to the case of three crossing levels, and they can be used to describe a number of physical phenomena.