Chapter 1 introduces several of the common principles, techniques and approximations that will be employed throughout the text. Classically, the Hamiltonian is the sum of kinetic energy and potential energy. In quantum mechanics, it is an operator that, by operating on the statefunction, leads to the energy observable. The chapter begins with a preliminary description of the crystal’s Hamiltonian and then introduces approximation techniques that permit useful solutions. Beginning with the simple jellium model, Hartree and Hartree-Fock approaches are developed, exchange interactions and correlation effects are explored, and both time-independent perturbation and time-dependent perturbation techniques discussed. Examples illustrate scattering by perturbation as well as adiabatic evolution. The centrality of fast-and-slow interactions is stressed, the Born-Oppenheimer approximation is illustrated through the configuration coordinate diagram, and interacting electron systems are analyzed. The multi-electron aspects are stressed by discussing static screening, dynamic screening and the meaning of permittivity therein.
