Stimulated and spontaneous transitions

Einstein considered that the radiation was also able to induce the molecule in the upper state to undergo a transition to the lower state and hence to generate a photon of frequency v. Thus, he wrote the rate of this stimulated emission as 

The constant A is the Einstein coefficient of spontaneous emission. It can be shown that the coefficients of stimulated absorption and emission are equal and that the coefficient of spontaneous emission is related to them by 

The presence of in this relation implies that spontaneous emission can be largely ignored at the relatively low frequencies of vibrational transitions but may be important for transitions in the visible and ultraviolet regions. We shall see later (Sections 12.9 and 12.10) that spontaneous emission accounts for the phenomena of fluorescence and phosphorescence. Stimulated emission underlies the functioning of lasers ( laser is an acronym formed from light ampliflcation by the stimulated emission of radiation ). 

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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... 

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