Basic Mathematics.- Basic Mathematical Background: Introduction.- Representation Theory and Basic Theorems.- Character of a Representation.- Basis Functions.- Introductory Application to Quantum Systems.- Splitting of Atomic Orbitals in a Crystal Potential.- Application to Selection Rules and Direct Products.- Molecular Systems.- Electronic States of Molecules and Directed Valence.- Molecular Vibrations, Infrared, and Raman Activity.- Application to Periodic Lattices.- Space Groups in Real Space.- Space Groups in Reciprocal Space and Representations.- Electron and Phonon Dispersion Relation.- Applications to Lattice Vibrations.- Electronic Energy Levels in a Cubic Crystals.- Energy Band Models Based on Symmetry.- Spin-Orbit Interaction in Solids and Double Groups.- Application of Double Groups to Energy Bands with Spin.- Other Symmetries.- Time Reversal Symmetry.- Permutation Groups and Many-Electron States.- Symmetry Properties of Tensors.
About the Author:

M. S. Dresselhaus received her Ph.D. in Physics from the University of Chicago, in 1958. An Institute Professor at the Massachusetts Institute of Technology, she has been active in many aspects of materials research with particular emphasis on carbon science including nanostructures such as carbon nanotubes, but also including bismuth nanowires and other materials systems relevant to low dimensional thermoelectricity. She is the recipient of the National Medal of Science and 21 honorary degrees worldwide. She served as the Director of the Office of Science at the DOE in 2000--2001 and co-chaired a DOE report "Basic Research Needs for the Hydrogen Economy (2003).

G. Dresselhaus received his Ph.D. in Physics from the University of California, Berkeley, CA in 1955. He was a faculty member at the University of Chicago, and assistant professor at Cornell before joining MIT Lincoln Laboratory in 1960 as a staff member. In 1976 he assumed his current senior staff position at the MIT Francis Bitter Magnet Laboratory. His area of interest is the electronic structure of nanomaterials and he has co-authored with M.S. Dresselhaus several books on fullerenes, nanowires, and nanotubes.

A. Jorio received his Ph.D in Physics from the Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil, in 1999. He worked with Phase Transitions on Incommensurate Crystals, and he spent one year at the Institute Laue-Langevin (ILL), Grenoble, France. He also spent two years (2000 and 2001) as a post-doc at the Massachusetts Institute of Technology (MIT), Cambridge, USA, working with Raman Spectroscopy of Carbon Nanotubes. In 2001 he received the PROFIX Fellowship from the Brazilian Science Foundation CNPq, and returned to Brazil. He is a Professor of Physics at UFMG since 2002. Jorio's research interests focus on resonance Raman spectroscopy techniques and the photophysics of nanostructures.