Symmetry Of Many Electron Systems

Symmetry of Many-Electron Systems discusses the group-theoretical methods applied to physical and chemical problems. Group theory allows an individual to analyze qualitatively the elements of a certain system in scope. The text evaluates the characteristics of the Schrodinger equations. It is proved that some groups of continuous transformation from the Lie groups are useful in identifying conditions and in developing wavefunctions. A section of the book is devoted to the utilization of group-theoretical methods in quantal calculations on many-electron systems. The focus is on the use of group-theoretical methods to the classification and calculation of states of molecule. A chapter of the book gives a comprehensive discussion of the fractional parentage method. This application is used in atomic and nuclear spectroscopy. The method of employing coordinate wave functions is explained. The standard Young-Yamanouchi orthogonal representation is presented completely. The book will provide useful guides for physicists, chemists, engineers, students, and researchers in the field of physics.

This volume continues the series of proceedings of summer schools on theoretical physics related to various aspects of the structure of condensed matter, and to appropriate mathematical methods for an adequate description. Three main topics are covered: (i) symmetric and unitary groups versus electron correlations in multicentre systems; (ii) conformal symmetries, the Bethe ansatz and quantum groups; (iii) paradoxes of statistics, space-time, and time quantum mechanics. Problems considered in previous schools are merged with some new developments, like statistics with continuous Young diagrams, the existence and structure of energy bands in solids with fullerenes, membranes and some coverings of graphite sheets, or vortex condensates with quantum counterparts of Maxwell lows.

The contents survey the achievements and research problems connected with an adequate description of condensed matter structure, its phases and other properties in terms of appropriate mathematical tools. The focus is on the following topics: Action of groups on sets and broken symmetries; Racah-Wigner approach to vibrations, electronic states, correlations and superconductivity in multicenter systems; crystallography and its extension.

This volume continues the series of proceedings of summer schools on theoretical physics related to various aspects of the structure of condensed matter, and to appropriate mathematical methods for an adequate description. Three main topics are covered: (i) symmetric and unitary groups versus electron correlations in multicentre systems; (ii) conformal symmetries, the Bethe ansatz and quantum groups; (iii) paradoxes of statistics, space-time, and time quantum mechanics. Problems considered in previous schools are merged with some new developments, like statistics with continuous Young diagrams, the existence and structure of energy bands in solids with fullerenes, membranes and some coverings of graphite sheets, or vortex condensates with quantum counterparts of Maxwell lows.

Computational Physics is designed to provide direct experience in the computer modeling of physical systems. Its scope includes the essential numerical techniques needed to "do physics" on a computer. Each of these is developed heuristically in the text, with the aid of simple mathematical illustrations. However, the real value of the book is in the eight Examples and Projects, where the reader is guided in applying these techniques to substantial problems in classical, quantum, or statistical mechanics. These problems have been chosen to enrich the standard physics curriculum at the advanced undergraduate or beginning graduate level. The book will also be useful to physicists, engineers, and chemists interested in computer modeling and numerical techniques. Although the user-friendly and fully documented programs are written in FORTRAN, a casual familiarity with any other high-level language, such as BASIC, PASCAL, or C, is sufficient. The codes in BASIC and FORTRAN are available on the web at http://www.computationalphysics.info. They are available in zip format, which can be expanded on UNIX, Window, and Mac systems with the proper software. The codes are suitable for use (with minor changes) on any machine with a FORTRAN-77 compatible compiler or BASIC compiler. The FORTRAN graphics codes are available as well. However, as they were originally written to run on the VAX, major modifications must be made to make them run on other machines.

The Symposium "Symmetries in Science VII: Spectrum Generating Algebras and Dynamic Symmetries in Physics" was held at the Southern Illinois University at Carbondale in Niigata, Japan Campus, during the period August 28-31, 1992. The Symposium was held in honor of Professor Francesco lachello on the occasion of his 50th birthday. We wish to thank the colleagues and friends of Franco for their participation in the Symposium as well as for contributing articles to this volume honoring him. It was their commitment and involvement which made this Symposium a success. We also wish to thank Dr. Jared H. Dorn, the director of SIUC-N, for his support in the planning and the execution of the Symposium. Moreover we wish to thank Mayor Nobuo Kumakura of Nakajo town and Mr. Kaichi Suzuki of the school entity "The Pacific" for their friendly support. Bruno Gruber, SIUC-N Takaharu Otsuka, University of Tokyo v LAUDATIO ON THE OCCASION OF THE 50TH BIRTHDAY OF PROFESSOR FRANCESCO IACHELLO I first met Franco lachello in 1974. Driving a smart Alfa-Romeo, he came to meet me at the station at Groningen where I was to spend a summer conducting research.

This volume provides an adequate mathematical description of solid state properties. It concentrates on group action methods, generalized statistics and molecular symmetries (unitary and symmetric groups).