Remarks on the semi-classical theory of three state system

The semi-classical solution of the three state system is considered to study the population inversion at and away from resonance. At resonance, it is shown that if the system is initially populated either in the upper or in the lower level, then the population oscillation occurs in a way which is quite different from that if it is initially populated in the middle state. At off resonance, there is gradual suppression of the population in the excited states and in the asymptotic limit of the detuning, the system returns to its initial state.