Einsteins treatment of stimulated

We must now consider how the stimulated emission and absorption of radiation are treated in the case of a real atom. The relations between the probability of stimulated and spontaneous transitions were derived by Einstein (1917) using arguments based on statistical mechanics. This paper, which appeared well before the development of a complete quantum theory, is available in translation in ter Haar 

This distribution is maintained by a dynamic equilibrium in which atoms continually make upward and downward transitions between the levels. We consider in particular the transitions between the levels i and k, shown in Fig.9.1, where k i atom can make an upward transition from the 

The rate at which upward transitions are occurring is given by 

The transition probability for downivard transitions from level k to level i, is the sum of the spontaneous 

The rate at which downward transitions occur is given by 

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