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The Recursion Method and Its Applications

Proceedings of the Conference, Imperial College, London, England September 13–14, 1984

  • Conference proceedings
  • © 1987

Overview

Editors:
  1. D. G. Pettifor
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  2. D. L. Weaire
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Part of the book series: Springer Series in Solid-State Sciences (SSSOL, volume 58)

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Table of contents (16 papers)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. Why Recur?

      • Volker Heine
      Pages 2-7

    3. The Recursive Solution of Schroedinger’s Equation

      • Roger Haydock
      Pages 8-20

  4. Related Methods

    1. Front Matter

      Pages 71-71
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    2. On a Generalized-Moments Method

      • J. P. Gaspard, Ph. Lambin
      Pages 72-83

    3. The Equation of Motion Method

      • A. MacKinnon
      Pages 84-90

    4. Use of Cyclic Matrices to Obtain Analytic Expressions for Crystals

      • Philippe Audit
      Pages 91-101

  5. Solid State Applications

    1. Front Matter

      Pages 103-103
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    2. Continued Fractions and Perturbation Theory: Application to Tight Binding Systems

      • P. Turchi, F. Ducastelle
      Pages 104-119

    3. Response Functions and Interatomic Forces

      • M. W. Finnis, D. G. Pettifor
      Pages 120-131

    4. The Recursion Method with a Non-Orthogonal Basis

      • R. Jones
      Pages 132-137

  6. Lanczos Method Applications

    1. Front Matter

      Pages 139-139
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    2. Hamiltonian Eigenvalues for Lattice Gauge Theories

      • A. C. Irving
      Pages 140-148

    3. The Lanczos Method in Lattice Gauge Theories

      • I. M. Barbour, N.-E. Behilil, P. E. Gibbs, G. Schierholz, M. Teper
      Pages 149-164
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About this book

This volume reviews recent advances in the development and application of the recursion method in computational solid state physics and elsewhere. It comprises the invited papers which were presented at a two-day conference at Imperial College, London during September 1984. The recursion method is based on the Lanczos algorithm for the tridiago­ nalisation of matrices, but it is much more than a straightforward numerical technique. It is widely regarded as the most elegant framework for a variety of calculations into which one may incorporate physical insights and a num­ ber of technical devices. The standard reference is Volume 35 of Solid State Physics, which contains all the early ideas of Heine, Haydock and others, upon which the method was established. The present volume provides the first review of subsequent developments. It also indicates where problems remain, or opinions differ, in the interpretation of the mathematical details or choice of practical techniques in applications. The field is still very li­ vely and much remains to be done, as the summary chapter clearly demonstra­ tes. We are grateful to the S. E. R. C. 's Collaborative Computational Project No. 9 on the electronic structure of solids and the Institute of Physics's Solid State Sub-committee for their sponsorship of the conference. We thank Angus MacKinnon for his help in conference organisation and Jacyntha Crawley for secretarial assistance. December 1984 David G. Pettifor Denis L. Weaire v Contents Part I Introduction Why Recur? By V.

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