Application of many-body theory to the one-electron problem of atoms, molecules and solids

Helmut Volz, Hermann Haken

Heimo G. Latal

ISBN: 0 471 96364 X Although the author claims to have written a `novel introduction' to the quantum theory of matter, this book is certainly just one of a wealth of books on that subject appearing on the market every year. What is really novel about the presentation is that the more `formal aspects' of quantum mechanics, especially a discussion of the Schrodinger equation, are relegated to an appendix, while in the text only specific solutions to that fundamental equation are discussed. On the other hand, the book certainly provides an extensive outline of various applications of quantum mechanics to atoms, molecules and solids. On the atomic level even the emission of light, spin and many electron atoms are treated; similarly on the molecular scale the most important aspects are presented. Almost one half of the book is devoted to the quantum theory of solids, and here the range of topics includes, of course, the band model and its various implications, but also surfaces and non-crystalline solids. Due to the aim of the book the author had to present various complex situations in an abbreviated form, thereby sometimes losing the rigour of the necessary proof of the statements. But, taken altogether, the book will provide the reader with an overall view, and sometimes an in-depth discussion, of the quantum world of atoms, molecules and solids. Somewhat distracting might be the large number of footnotes collected at the end of each chapter; of advantage, however, are the selections of problems there.

Michiel J. van Setten

The GW-method is a Green’s function based approach from the field of many body perturbation theory. It s most commonly used to perturbatively correct the electronic structure obtained from, for instance, density functional theory calculations. Formally derived already fifty years ago the first applications date back thirty years and only this decennium the method has become a standard approach for solid-state applications. The application to molecular systems is however still in an early stage. In the first part of this seminar the basic concepts of the GW method are introduced and the general problems are presented. In the second part the specific techniques and approached for the application to molecular systems are discussed. Finally we come back to solids and discuss the automatization of GW with the aim of high through put computation.

John C. Inkson

William Marias Malisoff

The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect (the phenomenon of the deflection of electrons at low speeds being less than at higher speeds in atomic collisions), and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra.

Gnter Sauermann