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Foundations Of One Electron Theory Of Solids  

Original Title  Foundations Of One Electron Theory Of Solids 
Author  L. I. Yatrebov, A. A. Katsnelson 
Publication date 
1987 
Topics  physics, mir publishers, solids, quantum mechanics, pseudopotential, crystal structure, crystals, atoms, alloys, imperfections, nearly free electron model, models, potential, scattering theory, pseudism, lattice vibrations, OPW approach, stability, perturbation theory, green’s function 
Collection  mirtitles, additional_collections 
Book Type  EBook 
Material Type  Book 
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In this book the behavior of electrons in a crystal is described in terms of the oneelectron model. Clearly, such a system would be best approached by a manybody formalism but because of mathe matical complexities only a very few real problems can be solved in this way. In the oneelectron model, each electron is considered separately as moving in the averaged field of the nuclei and all the other electrons. The resulting picture is simpler conceptually, much more tractable mathematically and, at the same time, is quite comprehensive, which makes the oneelectron model the most popu lar approach currently in use in solid state physics.
In presenting the material, we have tried to show the logic the theory followed as it was developed and, to some extent at least, to show the “scaffolding” used to build it. Whether or not we have succeeded is for the reader to judge.
The concept of pseudopotential, as we believe the reader will become convinced, is a direct consequence of quantummechanical scattering theory and we hope therefore that the book will be of interest not only for solid state specialists but also for a reader in volved in other “quantum” activities.
The book should be read more than once, though some places can perhaps be skipped over. Some of the topics were chosen be cause they arc likely to be important in the future development of the oneelectron model (these topics include scattering outside iso energetic surfaces, the concept of effective medium, and higher order perturbation corrections). Some problems are left, unobtrusive ly, for the reader to solve. For example, will a selfconsistent cal culation yield wider or narrower energy bands than those resulting from the nonselfconsistent treatment? To answer this question, the reader will have to master the material in Chapter 3. Our hope is that in the course of the book the reader will himself pose problems like this and we foresee the satisfaction he (or she) will take in solv ing them.
We hope that this book will be helpful for both theorists and ex perimentalists.
Contents
Preface 7
Introduction 11
Chapter 1. Principles of the oneelectron theory
Part 1 Theoretical principles of the pseudopotential method
Chapter 2. Scattering theory for “solidstate people”
2.1. Mathematical formalism 23
2.2. Scattering on an isolated potential 31
2.3. Pseudism and scattering 46
2.4. Bound states, pseudopotentials and the convergence of series 54
2.5. Scattering theory and potential form factors 61
Chapter 3. Theory of potential
3.1. Potential seen by an atomic electron 69
3.2. Dielectric screening 83
3.3. The selfconsistency of pseudopotential and additive screening 99
3.4. Muffintin potential 107
3.5. Average value of the screened potential 124
Chapter 4. Theory of pseudopotential form factors
4.1. Nonlocality, the energy dependence of form factors and perturbation theory 132
4.2. The OPW formfactor 144
4.3. Phaseshift form factors 157
4.4. Effective medium and pseudopotential form factors 173
Chapter 5. Pseudism and the secular equations of band theory
5.1. The Green’s function (or KKR) method 181
5.2. Pseudopotential secular equations 196
Part 2 The use of pseudopotential theory for crystalstructure calculations
Chapter 6. Formalism of crystalstructure energy calculations
6.1. Basic assumptions 205
6.2. Band structure energy of pure metals and binary alloys 205
6.3. Electrostatic energy 223
6.4. The total internal energy of an alloy: secondorder perturbation theory and the locality approximation 227
6.5. Higherorder perturbation analysis 232
6.6. OPW nonlocal alloy theory 236
Chapter 7. Pseudopotential theory of alloys. Structure stability application
7.1. Phase boundaries in terms of pseudopotential theory 241
7.2. Ordered phases, their structures, and existence conditions 245
7.3. Shortrange order problems 256
7.4. Crystal structure stability in the OPW approach 261
Chapter 8. Pseudopotential theory and imperfections in crystals
8.1. Introductory remarks 267
8.2. Crystal lattice vibrations 267 8.3. Static imperfections 279
Chapter 9. Principles of pseudopotential calculations of the properties of metals
9.1. Genera 287
9.2. Calculation of the atomic properties of crystalline metals and alloys 287
9.3. Transport properties of noncrystalline metals and alloys 297
References 317
Index 331

Foundations Of One Electron Theory Of Solids
 L. I. Yatrebov, A. A. Katsnelson
Foundations Of One Electron Theory Of Solids Original Title Foundations Of One Electron Th
Foundations Of One Electron Theory Of Solids
 L. I. Yatrebov, A. A. Katsnelson
Foundations Of One Electron Theory Of Solids Original Title Foundations Of One Electron Th