Multiple Scattering in Solids

Multiple Scattering in Solids by Antonios Gonis, William H. Butler.

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 differentia...

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Bibliographic Details
Main Authors: Gonis, Antonios (Author), Butler, William H. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2000.
Edition:1st ed. 2000.
Series:Graduate Texts in Contemporary Physics,
Springer eBook Collection.
Subjects:
Condensed matter.
Physics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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 Two Muffin-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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