Mathematical Methods for the Holstein Equation

Abstract In this chapter, we will discuss various methods for solving this equation. This chapter, as well as the following, is concentrated on the mathematical methods. The physical interpretation of the results will be given in Chapter 7. Holstein (1947) solved Eq. (5.1) by a variational technique. The symmetry of the Kernel function G(r, r’) = G(r’, r) permits this formulation of Eq. (5.1) as a variational problem.