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Preface | |

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Electrons in one-dimensional periodic potentials | |

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The Bloch theorem for one-dimensional periodicity | |

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Energy levels in a periodic array of quantum wells | |

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Electron tunneling and energy bands | |

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Transmission and reflection of electrons through an arbitrary potential | |

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Electron tunneling through a periodic potential | |

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The tight-binding approximation | |

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Expansion in localized orbitals | |

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Tridiagonal matrices and continued fractions | |

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Plane waves and nearly free-electron approximation | |

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Expansion in plane waves | |

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The Mathieu potential and the continued fraction solution | |

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Some dynamical aspects of electrons in band theory | |

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Further reading | |

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Geometrical description of crystals: direct and reciprocal lattices | |

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Simple lattices and composite lattices | |

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Periodicity and Bravais lattices | |

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Simple and composite crystal structures | |

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Geometrical description of some crystal structures | |

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Wigner-Seitz primitive cells | |

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Reciprocal lattices | |

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Definitions and basic properties | |

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Planes and directions in Bravais lattices | |

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Brillouin zones | |

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Translational symmetry and quantum mechanical aspects | |

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Translational symmetry and Bloch wavefunctions | |

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The parametric k [times] p Hamiltonian | |

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Cyclic boundary conditions | |

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Special k points for averaging over the Brillouin zone | |

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Density-of-states and critical points | |

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Further reading | |

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The Sommerfeld free-electron theory of metals | |

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Quantum theory of the free-electron gas | |

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Fermi-Dirac distribution function and chemical potential | |

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Electronic specific heat in metals and thermodynamic functions | |

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Thermionic emission from metals | |

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Outline of statistical physics and thermodynamic relations | |

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Microcanonical ensemble and thermodynamic quantities | |

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Canonical ensemble and thermodynamic quantities | |

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Grand canonical ensemble and thermodynamic quantities | |

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Fermi-Dirac and Bose-Einstein statistics for independent particles | |

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Modified Fermi-Dirac statistics in a model of correlation effects | |

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Further reading | |

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The one-electron approximation and beyond | |

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Introductory remarks on the many-electron problem | |

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The Hartree equations | |

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Identical particles and determinantal wavefunctions | |

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Matrix elements between determinantal states | |

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The Hartree-Fock equations | |

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Variational approach and Hartree-Fock equations | |

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Ground-state energy, ionization energies and transition energies | |

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Hartree-Fock equations and transition energies in closed-shell systems | |

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Hartree-Fock-Slater and Hartree-Fock-Roothaan approximations | |

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Overview of approaches beyond the one-electron approximation | |

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Electronic properties and phase diagram of the homogeneous electron gas | |

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The density functional theory and the Kohn-Sham equations | |

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Bielectronic integrals among spin-orbitals | |

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Outline of second quantization formalism for identical fermions | |

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An integral on the Fermi sphere | |

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Further reading | |

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Band theory of crystals | |

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Basic assumptions of the band theory | |

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The tight-binding method (LCAO method) | |

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Description of the method for simple lattices | |

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Description of the tight-binding method for composite lattices | |

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Illustrative applications of the tight-binding scheme | |

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The orthogonalized plane wave (OPW) method | |

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The pseudopotential method | |

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The cellular method | |

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The augmented plane wave (APW) method | |

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Description of the method | |

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Expression and evaluation of the matrix elements of the APW method | |

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The Green's function method (KKR method) | |

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Scattering integral equation for a generic potential | |

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Scattering integral equation for a periodic muffin-tin potential | |

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Expression and evaluation of the structure coefficients | |

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Other methods and developments in electronic structure calculations | |

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The linearized cellular methods | |

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The Lanczos or recursion method | |

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Modified Lanczos method for excited states | |

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Renormalization method for electronic systems | |

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Further reading | |

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Electronic properties of selected crystals | |

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Band structure and cohesive energy of rare-gas solids | |

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General features of band structure of rare-gas solids | |

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Cohesive energy of rare-gas solids | |

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Electronic properties of ionic crystals | |

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Introductory remarks and Madelung constant | |

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Considerations on bands and bonds in ionic crystals | |

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Covalent crystals with diamond structure | |

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Band structures and Fermi surfaces of some metals | |

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Further reading | |

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Excitons, plasmons and dielectric screening in crystals | |

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Exciton states in crystals | |

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Plasmon excitations in crystals | |

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General considerations on the longitudinal dielectric function | |

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Static dielectric screening in metals with the Thomas-Fermi model | |

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Static dielectric screening in metals with the Lindhard model | |

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Dynamic dielectric screening in metals and plasmon modes | |

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Quantum expression of the longitudinal dielectric function in materials | |

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Quantum expression of the longitudinal dielectric function in crystals | |

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Longitudinal dielectric function and energy-loss of a fast charged particle | |

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Lindhard dielectric function for the free-electron gas | |

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Further reading | |

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Interacting electronic-nuclear systems and the adiabatic principle | |

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Electronic-nuclear systems and adiabatic potential-energy surfaces | |

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Non-degenerate adiabatic surface and nuclear dynamics | |

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Non-degenerate adiabatic surface and classical nuclear dynamics | |

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Non-degenerate adiabatic surface and quantum nuclear dynamics | |

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Degenerate adiabatic surfaces and Jahn-Teller systems | |

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Degenerate adiabatic surfaces and nuclear dynamics | |

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The Jahn-Teller effect for doubly degenerate electronic states | |

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The Jahn-Teller effect for triply degenerate electronic states | |

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The Hellmann-Feynman theorem and electronic-nuclear systems | |

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General considerations on the Hellmann-Feynman theorem | |

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Charge density and atomic forces | |

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Parametric Hamiltonians and Berry phase | |

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Macroscopic electric polarization in crystals and Berry phase | |

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Further reading | |

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Lattice dynamics of crystals | |

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Dynamics of monatomic one-dimensional lattices | |

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Dynamics of diatomic one-dimensional lattices | |

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Dynamics of general three-dimensional crystals | |

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Quantum theory of the harmonic crystal | |

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Lattice heat capacity. Einstein and Debye models | |

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Considerations on anharmonic effects and melting of solids | |

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Optical phonons and polaritons in polar crystals | |

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General considerations | |

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Lattice vibrations in polar crystals and polaritons | |

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Local field effects on polaritons | |

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Quantum theory of the linear harmonic oscillator | |

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Further reading | |

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Scattering of particles by crystals | |

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General considerations | |

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Elastic scattering of X-rays from crystals | |

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Elastic scattering of X-rays and Bragg diffraction condition | |

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Elastic scattering of X-rays and intensity of diffracted beams | |

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Inelastic scattering of particles and phonon spectra of crystals | |

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Compton scattering and electron momentum density | |

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Diffusion of particles by a single elastically-bound scatterer | |

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Dynamical structure factor of a single scattering center | |

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Dynamical structure factor of a three-dimensional harmonic oscillator | |

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Diffusion of particles by a crystal and effects of lattice vibrations | |

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Mossbauer effect | |

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Further reading | |

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Optical and transport properties in metals | |

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Macroscopic theory of optical constants in homogeneous materials | |

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The Drude theory of the optical properties of free carriers | |

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Transport properties and Boltzmann equation | |

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Static and dynamic conductivity in metals | |

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Static conductivity with the Boltzmann equation | |

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Frequency and wavevector dependence of the conductivity | |

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Anomalous skin effect | |

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Boltzmann treatment and quantum treatment of intraband transitions | |

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The Boltzmann equation in electric fields and temperature gradients | |

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The transport equations in general form | |

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Thermoelectric phenomena | |

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Further reading | |

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Optical properties of semiconductors and insulators | |

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Quantum expression of the transverse dielectric function in materials | |

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Optical constants of homogeneous media in the linear response theory | |

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Optical constants and Green's function of the electronic system | |

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Quantum theory of band-to-band optical transitions and critical points | |

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Indirect phonon-assisted transitions | |

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Two-photon absorption | |

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Exciton effects on the optical properties | |

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Fano resonances and absorption lineshapes | |

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Optical properties of vibronic systems | |

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Optical properties of the Frank-Condon vibronic model | |

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Optical properties of typical Jahn-Teller systems | |

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Transitions rates at first and higher orders of perturbation theory | |

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Further reading | |

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Transport in intrinsic and homogeneously doped semiconductors | |

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Fermi level and carrier density in intrinsic semiconductors | |

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Impurity levels in semiconductors | |

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Fermi level and carrier density in doped semiconductors | |

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Thermionic emission in semiconductors | |

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Non-equilibrium carrier distributions | |

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Drift and diffusion currents | |

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Generation and recombination of electron-hole pairs in semiconductors | |

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Solutions of typical transport equations in uniformly doped semiconductors | |

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Further reading | |

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Transport in inhomogeneous semiconductors | |

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Properties of the pn junction at equilibrium | |

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Current-voltage characteristics of the pn junction | |

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The bipolar junction transistor | |

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The junction field-effect transistor (JFET) | |

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Semiconductor heterojunctions | |

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Metal-semiconductor contacts and MESFET transistor | |

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The metal-oxide-semiconductor structure and MOSFET transistor | |

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Further reading | |

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Electron gas in magnetic fields | |

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Magnetization and magnetic susceptibility | |

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Energy levels and density-of-states of a free-electron gas in magnetic fields | |

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Energy levels of the two-dimensional electron gas in magnetic fields | |

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Energy levels of the three-dimensional electron gas in magnetic fields | |

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Orbital magnetic susceptibility and de Haas-van Alphen effect | |

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Orbital magnetic susceptibility of a two-dimensional electron gas | |

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Orbital magnetic susceptibility of a three-dimensional electron gas | |

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Spin paramagnetism of a free-electron gas | |

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Magnetoresistivity and classical Hall effect | |

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The quantum Hall effect | |

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Free energy of an electron gas in a uniform magnetic field | |

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Generalized orbital magnetic susceptibility of the free-electron gas | |

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Further reading | |

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Magnetic properties of localized systems and Kondo impurities | |

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Quantum mechanical treatment of magnetic susceptibility | |

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Magnetic susceptibility of closed-shell systems | |

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Permanent magnetic dipoles in atoms or ions with partially filled shells | |

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Paramagnetism of localized magnetic moments | |

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Localized magnetic states in normal metals | |

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Dilute magnetic alloys and the resistance minimum phenomenon | |

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Some phenomenological aspects | |

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The resistance minimum phenomenon | |

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Microscopic origin of the Kondo interaction: a molecular model | |

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Magnetic impurity in normal metals at very low temperatures | |

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Further reading | |

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Magnetic ordering in crystals | |

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Ferromagnetism and the Weiss molecular field | |

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Microscopic origin of the coupling between localized magnetic moments | |

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Antiferromagnetism in the mean field approximation | |

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Spin waves and magnons in ferromagnetic crystals | |

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The Ising model with the transfer matrix method | |

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The Ising model with the renormalization group theory | |

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The Stoner-Hubbard itinerant electron model for magnetism | |

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Further reading | |

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Superconductivity | |

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Some phenomenological aspects of superconductors | |

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The Cooper pair idea | |

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Ground state for a superconductor in the BCS theory at zero temperature | |

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Variational determination of the ground-state wavefunction | |

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Ground-state energy and isotopic effect | |

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Momentum distribution and coherence length | |

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Excited states of superconductors at zero temperature | |

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The Bogoliubov canonical transformation | |

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Persistent currents in superconductors | |

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Electron tunneling into superconductors | |

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Treatment of superconductors at finite temperature and heat capacity | |

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Diamagnetism of superconductors and Meissner effect | |

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The phenomenological London model | |

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Pippard electrodynamics and effective magnetic penetration depth | |

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Macroscopic quantum phenomena | |

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Order parameter in superconductors and Ginzburg-Landau theory | |

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Magnetic flux quantization | |

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Type-I and type-II superconductors | |

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Cooper pair tunneling between superconductors and Josephson effects | |

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The phonon-induced electron-electron interaction | |

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Further reading | |

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Subject index | |