Multiple Scattering in Solids (Graduate Texts in Contemporary Physics) - Hardcover

Gonis, Antonios; Butler, William H.

Hardcover

ISBN 10: 038798853X ISBN 13: 9780387988535

Publisher: Springer, 1999

Synopsis

The origins of multiple scattering theory (MST) can be traced back to Lord Rayleigh's publication of a paper treating the electrical resistivity of an ar­ ray of spheres, which appeared more than a century ago. At its most basic, MST provides a technique for solving a linear partial differential equa­ tion defined over a region of space by dividing space into nonoverlapping subregions, solving the differential equation for each of these subregions separately and then assembling these partial solutions into a global phys­ ical solution that is smooth and continuous over the entire region. This approach has given rise to a large and growing list of applications both in classical and quantum physics. Presently, the method is being applied to the study of membranes and colloids, to acoustics, to electromagnetics, and to the solution of the quantum-mechanical wave equation. It is with this latter application, in particular, with the solution of the SchrOdinger and the Dirac equations, that this book is primarily concerned. We will also demonstrate that it provides a convenient technique for solving the Poisson equation in solid materials. These differential equations are important in modern calculations of the electronic structure of solids. The application of MST to calculate the electronic structure of solid ma­ terials, which originated with Korringa's famous paper of 1947, provided an efficient technique for solving the one-electron Schrodinger equation.

About this title

Product Description

Unusual book

Synopsis

This book describes general techniques for solving linear partial differential equations by dividing space into regions to which the equations are independently applied and then assembling a global solution from the partial ones. It is intended for researchers and graduate students involved in calculations of the electronic structure of materials, but will also be of interest to workers in quantum chemistry, electron microscopy, acoustics, optics, and other fields. Multiple scattering theory is, in essence, an extension of Huygens's principle to quantum mechanics. In classical physics, it was introduced by Rayleigh to study propagation of heat and electricity in inhomogeneous media. In quantum theory it has been used to study a number of different phenomena, including LEED spectra, defects in crystalline and disordered media, transport phenomena, photoemission spectroscopy, and electronic-structure calculations. The book begins with an intuitive approach to scattering theory and then turns to partial waves and a formal development of multiple scattering theory, with applications to the solid state (muffin-tin potentials and space-filling cells).

The authors then present a variational derivation of the formalism and an augmented version of the theory. It concludes with a discussion of the relativistic formalism and a discussion of the Poisson equation. Appendices discuss Green's functions, spherical functions, Moller operators and the Lippmann-Schwinger equation, irregular solutions, and singularities in Green's functions.

Edition details

• Publisher: Springer
• Publication date: 1999
• Language: English
• ISBN 10: 038798853X
• ISBN 13: 9780387988535
• Binding: Hardcover
• Number of pages: 298