Quantum Mechanical Description of Solids

Abstract

Condensed matter is a many-body problem in quantum mechanics. The many-electron and many-atom systems are separated from each other by the adiabatic approximation. These two many-body problems are then treated differently: the electron problem in the Hartree-Fock approximation leading to single electron states and specifically to band structure for crystals; the atomic dynamics of crystals as collective excitations which when quantized lead to phonons. Collective excitations of electrons are then considered and plasmons formulated. Some general characteristics of quasi-particle and collective excitations will be discussed and inter-related where possible. In addition to intrinsic properties of solids, some of their extrinsic properties are treated theoretically, including the effects of applied stress on electronic states and vibrational levels of ions and molecules in crystals.

Supported in part by a grant from the Army Research Office-Durham and in part by a Humboldt Prize (Senior U.S. Scientist Award).