Multiple Scattering in Solids - Graduate Texts in Contemporary Physics Softcover Reprint of the Original 1st Ed. 2000 edition

Description for Sales People: 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. Table of Contents: 1 Introduction.- 1.1 Basic Characteristics of MST.- 1.2 Electronic Structure Calculations.- 1.3 The Aim of This Book.- References.- 2 Intuitive Approach to MST.- 2.1 Huygens Principle and MST.- 2.1.1 Informal Discussion: Point Scatterers.- 2.1.2 Formal Presentation.- 2.2 Time-Independent Green Functions.- References.- 3 Single-Potential Scattering.- 3.1 Partial-Wave Analysis of Single Potential Scattering.- 3.2 General Considerations.- 3.3 Spherically Symmetric Potentials.- 3.3.1 Free-Particle Solutions.- 3.3.2 The Radial Equation for Central Potentials..- 3.3.3 The Scattering Amplitude.- 3.3.4 Normalization of the Scattering Wave Function.- 3.3.5 Integral Expressions for the Phase Shifts.- 3.4 Nonspherical Potentials.- 3.4.1 Alternative Forms of the Solution.- 3.4.2 Direct Determination of thet-Matrix(*).- 3.5 Wave Function in the Moon Region.- 3.5.1 Displaced-Center Approach: Convex Cells.- 3.5.2 Displaced-Cell Approach: Convex Cells.- 3.5.3 Numerical Example: Convergence for Square Cell.- 3.5.4 Displaced-Cell Approach: Concave Cells (*).- 3.6 Effect of the Potential in the Moon Region.- 3.7 Convergence of Basis Function Expansions (*).- 3.7.1 First Justification.- 3.7.2 Second Justification.- References.- 4 Formal Development of MST.- 4.1 Scattering Theory for a Single Potential.- 4.1.1 The S-Matrix and the t-Matrix.- 4.1.2 t-Matrices and Green Functions.- 4.2 Two-Potential Scattering.- 4.2.1 An Integral Equation for thet-Matrix.- 4.3 The Equations of Multiple Scattering Theory.- 4.3.1 The Wave Functions of Multiple Scattering Theory.- 4.4 Representations.- 4.4.1 The Coordinate Representation.- 4.4.2 The Angular-Momentum Representation.- 4.4.3 Representability of the Green Function and the Wave Function.- 4.4.4 Example of Representability.- 4.4.5 The Representability Theorem.- 4.5 Muffin-Tin Potentials.- References.- 5 MST for Muffin-Tin Potentials.- 5.1 Multiple Scattering Series.- 5.1.1 The Angular-Momentum Representation.- 5.1.2 Electronic Structure of a Periodic Solid.- 5.2 The Green Function in MST.- 5.3 Impurities in MST.- 5.4 Coherent Potential Approximation.- 5.5 Screened MST.- 5.6 Alternative Derivation of MST.- 5.7 Korringa s Derivation.- 5.8 Relation to Muffin-Tin Orbital Theory.- 5.9 MST for EPublisher Marketing: 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."