Book contents
- Frontmatter
- PREFACE
- PREFACE TO THE SECOND EDITION
- Contents
- Chapter 1 Periodic Structures
- Chapter 2 Lattice Waves
- Chapter 3 Electron States
- Chapter 4 Static Properties of Solids
- Chapter 5 Electron-Electron Interaction
- Chapter 6 Dynamics of Electrons
- Chapter 7 Transport Properties
- Chapter 8 Optical Properties
- Chapter 9 The Fermi Surface
- Chapter 10 Magnetism
- Chapter 11 Superconductivity
- Bibliography
- Index
Chapter 5 - Electron-Electron Interaction
Published online by Cambridge University Press: 05 June 2013
- Frontmatter
- PREFACE
- PREFACE TO THE SECOND EDITION
- Contents
- Chapter 1 Periodic Structures
- Chapter 2 Lattice Waves
- Chapter 3 Electron States
- Chapter 4 Static Properties of Solids
- Chapter 5 Electron-Electron Interaction
- Chapter 6 Dynamics of Electrons
- Chapter 7 Transport Properties
- Chapter 8 Optical Properties
- Chapter 9 The Fermi Surface
- Chapter 10 Magnetism
- Chapter 11 Superconductivity
- Bibliography
- Index
Summary
‘The whole thing is a low put-up job on our noble credulity’ said Sam.
NORMAN LINDSAY, The Magic PuddingPerturbation formulation
The theory of electronic structure, as presented in Chapter 3, is a one-electron model; each electron is treated as an independent particle, moving in a well-defined potential, and the interactions between conduction electrons are ignored. But we know that these interactions are strong, and are of long range, being the Coulomb force between the charges and the so-called exchange force associated with the antisymmetry of the wave-functions.
Naively we assume that these interactions can be taken care of by a Hartree or Hartree–Fock self-consistent calculation that adjusts the atomic potentials for the charge distribution of the valence electrons (as well, of course, as the electrons in the closed shells of the ion cores). But this is not easy to do properly—and we may have to fall back on some assumption, like that used by Wigner and Seitz (§4.3), that the electron sees the potential of a singly charged ion in the cell where it happens to be, but that neighbouring cells are electrically neutral.
In recent years, therefore, a lot of effort has been expended on the many-body problem of a gas of electrons interacting via their Coulomb potential, and the basic effects of the interaction are now well understood. Much of the theory is expressed in complicated formal language; the main results are surprisingly simple, and can be derived by elementary arguments.
- Type
- Chapter
- Information
- Principles of the Theory of Solids , pp. 146 - 170Publisher: Cambridge University PressPrint publication year: 1972
- 1
- Cited by