Formalisms of Band Theory

This chapter discusses the crystal momentum representation (CMR) that is evidently analogous to the momentum representation of ordinary continuum mechanics. It describes the Wannier representation’ (WR), which is analogous to the coordinate representation. The chapter discusses the development of the Crystal momentum representation (CMR) ab initio and relates the other methods to it. These include the Kohn–Luttinger or modified crystal momentum representation (MCMR) and the Wannier Representation (WR). Wannier was interested in the problem of the large exciton that is similar to but more difficult than the usual type of problem to be attacked by the methods. Wannier introduced Wannier functions to have localized states to describe the system and later derived an equation for the relative motion of the hole and electron, which is very similar to the equations discussed in the chapter.