Operator Techniques

Abstract

In the first two sections of this chapter, we will have a brief look at a different approach to the solution of second order linear differential equations based upon operator techniques. Such techniques have been employed widely in physics and other fields of analysis. In quantum mechanics, one is often concerned with the time evolution operator u(t) which satisfies the differential equation of the type

$$\frac{{du(t)}}{{dt}} = Au$$

((1))

$$u(0) = 1$$

((2))

The Bloch equation, the master or rate equations in chemical kinetics and in statistical mechanics are cases in point.