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.
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A description of 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. Intended for researchers and graduates involved in calculations of the electronic structure of materials, this will also be of interest to workers in quantum chemistry, electron microscopy, acoustics, optics, and other fields. 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. The authors then present a variational derivation of the formalism and an augmented version of the theory, concluding 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.
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Taschenbuch. Zustand: Neu. Multiple Scattering in Solids | Antonios Gonis (u. a.) | Taschenbuch | xiii | Englisch | 2012 | Springer | EAN 9781461270805 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Artikel-Nr. 106118710
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9781461270805
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