Group Theory: Application to the Physics of Condensed Matter

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Springer Science & Business Media, Dec 13, 2007 - Science - 582 pages
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Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides in the transformation of many complex symmetry operations into a very simple linear algebra. This concise and class-tested book has been pedagogically tailored over 30 years MIT and 2 years at the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory in close connection with applications helps students to learn, understand and use it for their own needs. For this reason, the theoretical background is confined to the first 4 introductory chapters (6-8 classroom hours). From there, each chapter develops new theory while introducing applications so that the students can best retain new concepts, build on concepts learned the previous week, and see interrelations between topics as presented. Essential problem sets between the chapters also aid the retention of the new material and for the consolidation of material learned in previous chapters. The text and problem sets have proved a useful springboard for the application of the basic material presented here to topics in semiconductor physics, and the physics of carbon-based nanostructures.

 

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It is very hard for me!!!! I have been befuddle all the time!!!

Contents

Introduction
3
Representation Theory and Basic Theorems
15
Character of a Representation
29
Basis Functions 57
56
Splitting of Atomic Orbitals in a Crystal Potential 79
77
Application to Selection Rules and Direct Products
97
Electronic States of Molecules and Directed Valence 113
112
Molecular Vibrations Infrared and Raman Activity
147
SpinOrbit Interaction in Solids and Double Groups
337
Application of Double Groups to Energy Bands with Spin
367
Time Reversal Symmetry 403
402
Permutation Groups and ManyElectron States
431
Symmetry Properties of Tensors
455
A Point Group Character Tables
479
B TwoDimensional Space Groups 489
488
Tables for 3D Space Groups
499

Space Groups in Real Space 183
180
Space Groups in Reciprocal Space and Representations
209
Applications to Lattice Vibrations 241
239
Electronic Energy Levels in a Cubic Crystals
279
Energy Band Models Based on Symmetry 305
304
Tables for Double Groups
521
E Group Theory Aspects of Carbon Nanotubes
533
F Permutation Group Character Tables
543
Index
553
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Page 551 - OV KOVALEV. - Irreducible Representations of the Space Groups, Gordon and Breach, New York, (1965).

About the author (2007)

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.