Overview

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.

Full Product Details

Author:   Antonios Gonis ,  William H. Butler
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2000 ed.
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.330kg
ISBN:  

9780387988535

ISBN 10:   038798853
Pages:   285
Publication Date:   28 December 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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.- 2.2 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.- 3.4 Nonspherical Potentials.- 3.5 Wave Function in the Moon Region.- 3.6 Effect of the Potential in the Moon Region.- 3.7 Convergence of Basis Function Expansions (*).- References.- 4 Formal Development of MST.- 4.1 Scattering Theory for a Single Potential.- 4.2 Two-Potential Scattering.- 4.3 The Equations of Multiple Scattering Theory.- 4.4 Representations.- 4.5 Muffin-Tin Potentials.- References.- 5 MST for Muffin-Tin Potentials.- 5.1 Multiple Scattering Series.- 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 E < 0.- 5.10 The Convergence Properties of MST (*).- References.- 6 MST for Space-Filling Cells.- 6.1 Historical Development of Full-Cell MST.- 6.2 Derivations of MST for Space-Filling Cells.- 6.3 Full-Cell MST.- 6.4 The Green Function and Bloch Function.- 6.5 Variational Formalisms.- 6.6 Second Variational Derivation (*).- 6.7 Construction of the Wave Function.- 6.8 The Closure of Internal Sums (*).- 6.9 Numerical Results.- 6.10 Square Versus Rectangular Matrices (*).- References.- 7 Augmented MST(*).- 7.1 General Comments.- 7.2 MST with a Truncated Basis Set: MT Potentials.- 7.3 General Potentials.- 7.4 Green Functions and the Lloyd Formula.- 7.5 Numerical Study of TwoMuffin-Tin Potentials.- 7.6 Convergence of Electronic Structure Calculations.- References.- 8 Relativistic Formalism.- 8.1 General Comments.- 8.2 Generalized Partial Waves.- 8.3 Generalized Structure Constants.- 8.4 Free-Particle Solutions.- 8.5 Relativistic Single-Site Scattering Theory.- 8.6 Relativistic Multiple Scattering Theory.- References.- 9 The Poisson Equation.- 9.1 General Comments.- 9.2 Multipole Moments.- 9.3 Comparison with the Schrödinger Equation.- 9.4 Convex Polyhedral Cells.- 9.5 Numerical Results for Convex Cells.- 9.6 Concave Cells.- 9.7 Direct Analogy with MST.- References.- A Time-Dependent Green Functions.- B Time-Independent Green Functions.- C Spherical Functions.- C.1 The Spherical Harmonics.- C.2 The Bessel, Neumann, and Hankel Functions.- C.3 Solutions of the Helmholtz Equation.- References.- D Displacements of Spherical Functions References D.- References.- E The Two-Dimensional Square Cell.- E.1 Numerical Results (*).- References.- F Formal Scattering Theory.- F.1 General Comments.- F.2 Initial Conditions and the Møller Operators.- F.3 The Møller Wave Operators.- F.4 The Lippmann—Schwinger Equation.- References.- G Irregular Solutions to the Schrödinger Equation.- H Displacement of Irregular Solutions.- K Conversion of Volume Integrals.- L Energy Derivatives.- M Convergence of the Secular Matrix.- N Summary of MST.- N.1 General Framework.- N.2 Single Potential.- N.3 Multiple Scattering Theory.

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