# Light Induced Transition Probabilities and Rate Equations

One can assume rate constants for the absorption and emission of light quanta and describe ground state and excited state of molecules in a very generalized way. The absorption of photons transfers the system from the electronic ground state *N _{0}* to an electronically excited state

*N*

_{1}. We can generally assume to have an infinite number of such states. Recalling eq. 4 and eq. 5 we remember that the general master equation that denotes the dynamical formulation of the temporal change of states

*N*might be time dependent

_{t }*N*(t) and is therefore described by a differential equation that denotes the dynamical change in time

_{j}*N*(t) :

_{j}

with the transfer matrix *T _{jk}=T*. If we separate the supplying processes and the emptying processes we get:

This means that the description of our transfer matrix *T _{jk}=T* contains all processes that deliver

*N*(t) as off-diagonal elements and the process of the decaying

_{j}*N*(

_{j}*t*) as elements on the matrix diagonal. This description is very suitable to calculate time dependent spectra that result from fluorescence decay.

The full master equation denotes to

where the diagonal of the transfer matrix is filled with zeros. A generalized description of the motivation of the master equation was given in chapter 1.3 and can be reviewed in (Haken, 1990) and (Schmitt, 2011).