Novel Group Theoretical Methods for Electron Structure Theory

This book presents the induced representation method, a powerful technique in quantum mechanics with applications in condensed matter physics. After introducing the key concepts in group theory and representation theory necessary to understate the technique, the author goes on to explore applications in electron structure theory, namely: basis sets in clusters, normal vibrations, selection rules, two-electron wavefunctions, and space-group representations. This technique allows the simplification of standard techniques for the analysis of molecular orbitals and normal vibrations of molecules. A space group approach to the wavefunction of a Cooper pair based on the Anderson ansatz and Mackey-Bradley theorem is developed, and several applications are considered, namely group-theoretical nodes, non-symmorphic groups, and unification of the group theoretical and topological approaches to the structure of Cooper pairs in unconventional superconductors.

Point Groups and Wavefunctions in Molecules.- Magnetic Groups and Their Applications.- Induced Representations Method in the Theory of Electron Structure.- Cooper Pairs as Two-electron States in Crystals.

Victor G. Yarzhemsky, Dr.Sc., is a researcher at the N.S. Kurnakov Institute of General and Inorganic Chemistry (Russian Academy of Sciences) and at National Research Center “Kurchatov Institute”. His previous positions include a  fellowship at Melbourne University, and Moscow Institute of Physics and Technology. His research interests include group-theoretical and ab initio methods for molecules and solids, and also many-electron effects in atomic photoionization. He was awarded the N.N. Semenov Medal by the Academy of Engineering Sciences of the Russian Federation and is the author of one previous book, Handbook of Theoretical Atomic Physics (Springer 2012) co-authored with M.Ya Amusia and L.V. Chernysheva.