Elements of Quantum Dynamics

Abstract

The dynamical equations for quantum systems, the Schroedinger equation for pure states and the density-matrix equation for mixed states, form the theoretical background for description of transport phenomena in systems with different kinds of elementary excitations (quasiparticles). Both single-particle formulation of these equations and many-particle formalism, which is required for the cases of interacting quasiparticles, are presented below. This chapter is not a systematic introduction to quantum theory. It contains only the description of some basic equations and definitions (probability of transitions, second quantization, and so on). The properties of concrete quasiparticles (electrons, phonons, and photons in different materials) and their interaction are also discussed in order to use the corresponding results in the next chapters.