Consider a two-level energy gap with electronic energy states $E_1$ & $E_2$ and associated population densities $n_1$ and $n_2$ with $E_2>E_1$.
In the derivation of the Einstein coefficients for Absorption, Spontaneous Emission and Stimulated Emission, textbooks/notes quite often make statements like the transition from $E_2$ to $E_1$ only depends on population density $n_2$. As an example, for the case of spontaneous decay, this clearly is just not true as there is a limit to the number of electrons occupying $E_1$ .
My question then is: how is this assumption justified? and/or how is the maximum value of $n_1$ taken into account in general LASER theory?
All comments welcome.