A Compendium of Solid State Theory

Preface to the Second Edition
Preface to the First Edition
Contents
1 Introduction
2 Non-Interacting Electrons
	2.1 Free Electrons
	2.2 Electron in Electric and Magnetic Fields
		2.2.1 Homogeneous, Constant Electric Field
		2.2.2 Homogeneous, Constant Magnetic Field
			2.2.2.1 Magnetization
		2.2.3 Motion in a One-Dimensional Potential Well
	2.3 Electrons in a Periodical Potential
		2.3.1 Crystal Lattice
		2.3.2 Bloch Functions
		2.3.3 Periodical Boundary Conditions
		2.3.4 The Approximation of Quasi-Free Electrons
		2.3.5 The Kronig–Penney Model
		2.3.6 Band Extrema, kp: Perturbation Theory and Effective Mass
		2.3.7 Wannier Functions and Tight-Binding Approximation
		2.3.8 Bloch Electron in a Homogeneous Electric Field
	2.4 Electronic Occupation of States in a Crystal
		2.4.1 Ground State Occupation of Bands: Conductors and Insulators
		2.4.2 Spin–Orbit Coupling and Valence Band Splitting
	2.5 Electron States Due to Deviations from Periodicity
		2.5.1 Effective Mass Approximation
		2.5.2 Intrinsic Semiconductors at Finite Temperatures
		2.5.3 Ionic Impurities
		2.5.4 Extrinsic Semiconductors at Finite Temperatures: Acceptors and Donors
	2.6 Semiconductor Contacts
		2.6.1 Electric Field Penetration into a Semiconductor
		2.6.2 p–n Contact
3 Electron–Electron Interaction
	3.1 The Exciton
		3.1.1 Wannier Exciton
		3.1.2 Exciton Beyond the Effective Mass Approximation
	3.2 Many-Body Approach to the Solid State
		3.2.1 Self-Consistent Approximations
		3.2.2 Electron Gas with Coulomb Interactions
		3.2.3 The Electron–Hole Plasma
		3.2.4 Many-Body Perturbation Theory of Solid State
		3.2.5 Adiabatic Perturbation Theory
4 Phonons
	4.1 Lattice Oscillations
	4.2 Classical Continuum Phonon-Model
		4.2.1 Optical Phonons in Polar Semiconductors
		4.2.2 Optical Eigenmodes
		4.2.3 The Electron–Phonon Interaction
			4.2.3.1 The Franck–Condon Effect
			4.2.3.2 The Quantized Interaction of Electrons with Phonons
5 Transport Theory
	5.1 Non-Equilibrium Phenomena
	5.2 Classical Solvable Model of an Electron in a d.c. Electric Field Interacting with Phonons
	5.3 The Boltzmann Equation
		5.3.1 Classical Conductivity
	5.4 Kinetic Coefficients
	5.5 Master and Rate Equations
		5.5.1 Master Equations
		5.5.2 Rate Equations
	5.6 Hopping Transport
		5.6.1 Hopping Diffusion on a Periodic Cubic Lattice
		5.6.2 Transverse Magneto-Resistance in Ultra-Strong Magnetic Field
		5.6.3 Seebeck Coefficient for Hopping Conduction on Random Localized States
6 Optical Properties
	6.1 Linear Response to a Time-Dependent External Perturbation
	6.2 Equilibrium Linear Response
	6.3 Dielectric Response of a Coulomb Interacting Electron System
	6.4 The Full Nyquist Theorem
	6.5 Dielectric Function of an Electron Plasma in the Hartree Approximation
	6.6 The Transverse, Inter-Band Dielectric Response of an Electron–Hole Plasma
	6.7 Ultra-Short-Time Spectroscopy of Semiconductors
	6.8 Third Order Non-Linear Response
	6.9 Differential Transmission
	6.10 Four Wave Mixing
7 Phase Transitions
	7.1 The Heisenberg Model of Ferro-Magnetism
	7.2 Bose Condensation
		7.2.1 Bose Condensation in Real Time
	7.3 Bogoliubov\'s Self-Consistent Model of Repulsive Bosons at T=0
	7.4 Time-Dependent Bogoliubov and Gross–Pitaevskii Equations
	7.5 Superconductivity
		7.5.1 The Phenomenological Theory of London
	7.6 Superconducting Phase Transition in a Simple Model of Electron–Electron Interaction
		7.6.1 Meissner Effect Within Equilibrium Linear Response
		7.6.2 The Case of a Contact Potential: The Bogoliubov–de Gennes Equation
8 Low Dimensional Semiconductors
	8.1 Exciton in 2D
	8.2 Motion of a 2D Electron in a Strong Magnetic Field
	8.3 Coulomb Interaction in 2D in a Strong Magnetic Field
		8.3.1 Classical Motion
		8.3.2 Quantum Mechanical States
9 Extension of the Solid-State Hamiltonian: Current–Current Interaction Terms of Order 1/c2
	9.1 Classical Approach
	9.2 The Second Quantized Version
10 Field-Theoretical Approach to the Non-Relativistic Quantum Electrodynamics
	10.1 Field Theory
	10.2 Classical Maxwell Equations Coupled to a Quantum Mechanical Electron
	10.3 Classical Lagrange Density for the Maxwell Equations Coupled to a Quantum Mechanical Electron
	10.4 The Classical Hamiltonian in the Coulomb Gauge
	10.5 Quantization of the Hamiltonian
	10.6 Derivation of the 1/c2 Hamiltonian
11 Shortcut of Theoretical Physics
	11.1 Classical Mechanics
	11.2 One-Particle Quantum Mechanics
		11.2.1 Dirac\'s ``bra/ket\'\' Formalism
	11.3 Perturbation Theory
		11.3.1 Stationary Perturbation
		11.3.2 Time-Dependent Adiabatic Perturbation
	11.4 Many-Body Quantum Mechanics
		11.4.1 Configuration Space
		11.4.2 Fock Space (Second Quantization)
			11.4.2.1 Fermions
			11.4.2.2 Bosons
	11.5 Density Matrix (Statistical Operator)
	11.6 Classical Point-Like Charged Particles and Electromagnetic Fields
12 Homework
	12.1 The Kubo Formula
	12.2 Ideal Relaxation
	12.3 Rate Equation for Bosons
	12.4 Bose Condensation in a Finite Potential Well