Many-Body Theory of Solids [E-Book] : An Introduction / by John C. Inkson.
here exists a gap in the present literature on quantum mechanics T and its application to solids. It has been difficult to find an intro ductory textbook which could take a student from the elementary quan tum mechanical ideas of the single-particle Schrodinger equations, through the formalism and...
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Full text |
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Personal Name(s): | Inkson, John C., author |
Imprint: |
Boston, MA :
Springer,
1984
|
Physical Description: |
X, 334 p. online resource. |
Note: |
englisch |
ISBN: |
9781475702262 |
DOI: |
10.1007/978-1-4757-0226-2 |
Subject (LOC): |
- 1. The Interacting System
- 1.1. The Basic Problem
- 1.2. The Jellium Solid
- 1.3. Hartree Theory—The Sommerfeld Model
- 1.4. Hartree-Fock
- 1.5. Exchange and Correlation Holes
- 1.6. Correlation Effects and the Thomas-Fermi Model
- Problems
- 2. Green’s Functions of the Single-Particle Schrödinger Equation
- 2.1. Green’s Functions of the Schrödinger Equation
- 2.2. Green’s Functions and Perturbation Theory
- 2.3. Time-Dependent Green’s Functions
- 2.4. Green’s Function Diagrams
- 2.5. Green’s Functions or Wave Functions?
- Problems
- 3. Quantization of Waves (Second Quantization)
- 3.1. Waves and Particles
- 3.2. The Linear Chain of Atoms
- 3.3. The General Quantization of a Wave System
- 3.4. Quantization of the Electromagnetic Field
- 3.5. Elementary Excitations and “Particles”
- 3.6. Perturbations and the Elementary Excitations
- 3.7. Summary
- Problems
- 4. Representations of Quantum Mechanics
- 4.1. Schrödinger Representation
- 4.2. Heisenberg Representation
- 4.3. Interaction Representation
- 4.4. Occupation Number Representation
- 4.5. Interaction between Waves and Particles
- 4.6. Field Operators
- Problems
- 5. Interacting Systems and Quasiparticles
- 5.1. Single-Particle States
- 5.2. Absorbing Media
- 5.3. Exact and Approximate Eigenstates
- 5.4. Landau Quasiparticles
- Problems
- 6. Many-Body Green’s Functions
- 6.1. Definition of the Many-Body Green’s Function
- 6.2. Relationship to Single-Particle Green’s Function
- 6.3. Energy Structure and the Green’s Function
- 6.4. The Lehman Representation and Quasiparticles
- 6.5. Expectation Values
- 6.6. Equation of Motion for the Green’s Function
- 6.7. Hartree and Hartree-Fock Approximations
- 6.8. The Self-Energy
- Problems
- 7. The Self-Energy and Perturbation Series
- 7.1. Functional Derivatives and the Calculation of G and ?
- 7.2. Iterative Solution for the Green’s Function and Self-Energy
- 7.3. Screening and the Perturbation Series
- 7.4. The Screened Interaction and Selective Summations
- 7.5. The Uniform System
- Problems
- 8. Diagrammatic Interpretation of the Green’s Function Series
- 8.1. Diagrammatic Interpretation of the Perturbation Series
- 8.2. Diagrammatic Expansion
- 8.3. Infinite Series and Irreducible Diagrams
- 8.4. The Hartree Potential
- 8.5. The Uniform System
- 8.6. Rules for Evaluating Diagrams
- 8.7. Selective Summations
- 8.8. Practical Aspects of Diagrammatics
- Problems
- 9. The Normal System
- 9.1. The Jellium Solid Response Function
- 9.2. The Self-Energy (Physical Considerations)
- 9.3. Evaluation of the Self-Energy and Quasiparticle Properties
- 9.4. Landau Quasiparticles
- 9.5. Insulating Systems
- 9.6. Surfaces
- Problems
- 10. Thermal Effects on the Green’s Function
- 10.1. The Density Matrix
- 10.2. Statistical Mechanics
- 10.3. The “Thermal” Heisenberg Representation
- 10.4. Evaluation of the Perturbation Expansion
- 10.5. Periodicity of G and the Extension to Energy Dependency
- 10.6. Real-Time Thermal Green’s Functions
- Problems
- 11. Boson Particles
- 11.1. Collective Excitations in Solids
- 11.2. Electron-Phonon System
- 11.3. Plasmons and the Total Interaction
- 11.4. Boson Systems with a Condensate
- Problems
- 12. Special Methods
- 12.1. The Density Functional Method (Nearly Uniform Electron Gases)
- 12.2. Highly Localized Systems (Anderson-Hubbard Models)
- 12.3. Canonical Transformations
- 12.4. Mean-Field Theory
- Problems
- 13. Superconductivity
- 13.1. Cooper Pairs
- 13.2. Canonical Transformations
- 13.3. Propagator Approach
- Problems
- Appendix: List of Symbols.