The random walk problem revisited

The one-dimensional random walk problem described by Eq. (8.69) was discussed in Section 7.3. It was pointed out that summing either side of this equation over 

Many science texts refer to a 1928 paper by W. Pauli [W. Pauli, Festschrift zum 60. Geburtstage A. Sommerfelds (Hirzel, Leipzig, 1928) p. 30] as the first derivation of this type of Kinetic equation. Pauh has used this approach to construct a model for the time evolution of a many-sate quantum system, using transition rates obtained from quantum perturbation theory. 

More can be achieved by introducing the generating function, defined by  

We can get an equation for the time evolution of F by multiplying the master equation (8.69) by 5 and summing overall n. Using E -00 - bO = sFis) 

Problem 8.7. Equation (8.81) implies that F(5 = 1, Z) = 1 for all Z. Using the definition of the generating function show that this result holds generally, not only for the generating function of Eq. (8.69). 

---