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Eschrig H. The Fundamentals of Density Functional Theory

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Eschrig H. The Fundamentals of Density Functional Theory
B.G. Teubner Verlagsgesellschaft Stuttgart- Leipzig, 1996. — 204 p.
This regular series includes the presentation of recent research developments of strong interest as well as comprehensive treatments of important selected topics of physics. One of the aims is to make new results of research available to graduate students and younger scientists, and moreover to all people who like to widen their scope and inform themselves about new developments and
trends.
A larger part of physics and applications of physics and also its application in neighbouring sciences such as chemistry, biology and technology is covered. Examples for typical topics are: Statistical physics, physics of condensed matter, interaction of light with matter, mesoscopic physics, physics of surfaces and interfaces, laser physics, nonlinear processes and selforganization, ultrafast dynamics, chemical and biological physics, quantum measuring devices with ultimately high resolution and sensitivity, and finally applications of physics in interdisciplinary fields.
Contents
Introduction
Part I: Non-relativistic theory
Many-Body Systems
The Schrodinger Representation, N Fixed
The Momentum Representation, N Fixed
The Heisenberg Representation, N Fixed
Hartree-Fock Theory
The Occupation Number Representation, N Varying
Field Quantization

Density Matrices and Density Operators
Single-Particle Density Matrices
Two-Particle Density Matrices
Density Operators
Expectation Values and Density Matrices
The Exchange and Correlation Hole
The Adiabatic Principle
Coulomb Systems

Thomas-Fermi Theory

The Thomas-Fermi Functional and Thomas-Fermi Equation
The Thomas-Fermi Atom
The Thomas-Fermi Screening Length
Scaling Rules
Correction Terms

Hohenberg-Kohn Theory
The Basic Theorem by Hohenberg and Kohn
The Kohn-Shain Equation
The Link to the Hartree-Fock-Slater Approximation
Constrained Search Density Functionals
Ensemble State Density Functionals
Dependence on Particle Number N
Spin Polarization
Legendre Transformation
Elementary Introduction
Prelude on Topology
Prelude on Lebesgue Integral
Banach Space
Dual Space
Conjugate Functionals
The Functional Derivative
Lagrange Multipliers

Density Functional Theory by Lieb
Lieb's Density Functional
Resume so far
Dependence on Particle Number N
The Kohn-Sham Equation

Approximative Variants
The Homogeneous Electron Liquid
The Local Density Approximation
Generations of Kohn-Sham type equations
The Self-Interaction Correction

Part II: Relativistic theory
A Brief Introduction to Quantum Electrodynamics
Classical Electrodynamics
Lorentz Covariance
Lagrange Formalism Relativistic Kinematics
Relativtstic Mechanics
The Principles of Relativistic Quantum Theory
The Dirac Field
Current Density Functional Theory
QED Groundstate in a Static External Field
Current Density Functionals and Kohn-Sham-Dirac Equation
The Gordon Decomposition and Spin Density
Approximative Variants The Variational Solution of the Kohn-Sham-Dirac Equation
Bibliography
Index
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