TABLE OF CONTENTS In this section I will go through a few examples to illustrate the basic approach for describing incoherent interactions. I will take up the more general case of inflow and outflow in Section 10.3, but in this section I will assume all other states to be empty so that there is no exclusion principle to worry about and I will calculate the broadening (or the outflow), which can be identified with ?/ ?, ? being the lifetime of the state. This will include: (1) the photon-induced (radiative) lifetime due to atomic transitions; (2) the radiative lifetime due to interband transitions in semiconductors; and (3) the phonon-induced (non-radiative) lifetime due to intraband transitions in semiconductors (Fig. 10.2.1). The basic approach is to write down the interaction potential (see Eq. (10.1.14)), evaluate the coupling constants (see Eq. (10.1.15)), and obtain the broadening and hence the lifetime from Eq. (10.1.13).
From Eq. (10.1.13) it is apparent that the broadening is large when the argument of the delta function vanishes. How large it is at that point depends on the value of 0 + (see Section 8.4) that we choose to broaden each reservoir state. As we have seen in Chapter 8, the precise value of 0 + usually does not matter as long...
