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Solid State Physics

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ISBN-10: 012304460X

ISBN-13: 9780123044600

Edition: 2000

Authors: Giuseppe Pastori Grosso, Giuseppe Pastori Parravicini, Giuseppe Pastori Parravicini, Giuseppe Pastori Parravicini

List price: $142.00
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This volume explains to readers the newest advances in the area of condensed matter physics with mathematics. Examples are an integral part of the text, designed to apply the principles illustrated to current active topics of research.
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Book details

List price: $142.00
Copyright year: 2000
Publisher: Elsevier Science & Technology Books
Publication date: 2/14/2000
Binding: Hardcover
Pages: 714
Size: 5.98" wide x 9.02" long x 0.55" tall
Weight: 2.992
Language: English

Electrons in one-dimensional periodic potentials
The Bloch theorem for one-dimensional periodicity
Energy levels in a periodic array of quantum wells
Electron tunneling and energy bands
Transmission and reflection of electrons through an arbitrary potential
Electron tunneling through a periodic potential
The tight-binding approximation
Expansion in localized orbitals
Tridiagonal matrices and continued fractions
Plane waves and nearly free-electron approximation
Expansion in plane waves
The Mathieu potential and the continued fraction solution
Some dynamical aspects of electrons in band theory
Further reading
Geometrical description of crystals: direct and reciprocal lattices
Simple lattices and composite lattices
Periodicity and Bravais lattices
Simple and composite crystal structures
Geometrical description of some crystal structures
Wigner-Seitz primitive cells
Reciprocal lattices
Definitions and basic properties
Planes and directions in Bravais lattices
Brillouin zones
Translational symmetry and quantum mechanical aspects
Translational symmetry and Bloch wavefunctions
The parametric k [times] p Hamiltonian
Cyclic boundary conditions
Special k points for averaging over the Brillouin zone
Density-of-states and critical points
Further reading
The Sommerfeld free-electron theory of metals
Quantum theory of the free-electron gas
Fermi-Dirac distribution function and chemical potential
Electronic specific heat in metals and thermodynamic functions
Thermionic emission from metals
Outline of statistical physics and thermodynamic relations
Microcanonical ensemble and thermodynamic quantities
Canonical ensemble and thermodynamic quantities
Grand canonical ensemble and thermodynamic quantities
Fermi-Dirac and Bose-Einstein statistics for independent particles
Modified Fermi-Dirac statistics in a model of correlation effects
Further reading
The one-electron approximation and beyond
Introductory remarks on the many-electron problem
The Hartree equations
Identical particles and determinantal wavefunctions
Matrix elements between determinantal states
The Hartree-Fock equations
Variational approach and Hartree-Fock equations
Ground-state energy, ionization energies and transition energies
Hartree-Fock equations and transition energies in closed-shell systems
Hartree-Fock-Slater and Hartree-Fock-Roothaan approximations
Overview of approaches beyond the one-electron approximation
Electronic properties and phase diagram of the homogeneous electron gas
The density functional theory and the Kohn-Sham equations
Bielectronic integrals among spin-orbitals
Outline of second quantization formalism for identical fermions
An integral on the Fermi sphere
Further reading
Band theory of crystals
Basic assumptions of the band theory
The tight-binding method (LCAO method)
Description of the method for simple lattices
Description of the tight-binding method for composite lattices
Illustrative applications of the tight-binding scheme
The orthogonalized plane wave (OPW) method
The pseudopotential method
The cellular method
The augmented plane wave (APW) method
Description of the method
Expression and evaluation of the matrix elements of the APW method
The Green's function method (KKR method)
Scattering integral equation for a generic potential
Scattering integral equation for a periodic muffin-tin potential
Expression and evaluation of the structure coefficients
Other methods and developments in electronic structure calculations
The linearized cellular methods
The Lanczos or recursion method
Modified Lanczos method for excited states
Renormalization method for electronic systems
Further reading
Electronic properties of selected crystals
Band structure and cohesive energy of rare-gas solids
General features of band structure of rare-gas solids
Cohesive energy of rare-gas solids
Electronic properties of ionic crystals
Introductory remarks and Madelung constant
Considerations on bands and bonds in ionic crystals
Covalent crystals with diamond structure
Band structures and Fermi surfaces of some metals
Further reading
Excitons, plasmons and dielectric screening in crystals
Exciton states in crystals
Plasmon excitations in crystals
General considerations on the longitudinal dielectric function
Static dielectric screening in metals with the Thomas-Fermi model
Static dielectric screening in metals with the Lindhard model
Dynamic dielectric screening in metals and plasmon modes
Quantum expression of the longitudinal dielectric function in materials
Quantum expression of the longitudinal dielectric function in crystals
Longitudinal dielectric function and energy-loss of a fast charged particle
Lindhard dielectric function for the free-electron gas
Further reading
Interacting electronic-nuclear systems and the adiabatic principle
Electronic-nuclear systems and adiabatic potential-energy surfaces
Non-degenerate adiabatic surface and nuclear dynamics
Non-degenerate adiabatic surface and classical nuclear dynamics
Non-degenerate adiabatic surface and quantum nuclear dynamics
Degenerate adiabatic surfaces and Jahn-Teller systems
Degenerate adiabatic surfaces and nuclear dynamics
The Jahn-Teller effect for doubly degenerate electronic states
The Jahn-Teller effect for triply degenerate electronic states
The Hellmann-Feynman theorem and electronic-nuclear systems
General considerations on the Hellmann-Feynman theorem
Charge density and atomic forces
Parametric Hamiltonians and Berry phase
Macroscopic electric polarization in crystals and Berry phase
Further reading
Lattice dynamics of crystals
Dynamics of monatomic one-dimensional lattices
Dynamics of diatomic one-dimensional lattices
Dynamics of general three-dimensional crystals
Quantum theory of the harmonic crystal
Lattice heat capacity. Einstein and Debye models
Considerations on anharmonic effects and melting of solids
Optical phonons and polaritons in polar crystals
General considerations
Lattice vibrations in polar crystals and polaritons
Local field effects on polaritons
Quantum theory of the linear harmonic oscillator
Further reading
Scattering of particles by crystals
General considerations
Elastic scattering of X-rays from crystals
Elastic scattering of X-rays and Bragg diffraction condition
Elastic scattering of X-rays and intensity of diffracted beams
Inelastic scattering of particles and phonon spectra of crystals
Compton scattering and electron momentum density
Diffusion of particles by a single elastically-bound scatterer
Dynamical structure factor of a single scattering center
Dynamical structure factor of a three-dimensional harmonic oscillator
Diffusion of particles by a crystal and effects of lattice vibrations
Mossbauer effect
Further reading
Optical and transport properties in metals
Macroscopic theory of optical constants in homogeneous materials
The Drude theory of the optical properties of free carriers
Transport properties and Boltzmann equation
Static and dynamic conductivity in metals
Static conductivity with the Boltzmann equation
Frequency and wavevector dependence of the conductivity
Anomalous skin effect
Boltzmann treatment and quantum treatment of intraband transitions
The Boltzmann equation in electric fields and temperature gradients
The transport equations in general form
Thermoelectric phenomena
Further reading
Optical properties of semiconductors and insulators
Quantum expression of the transverse dielectric function in materials
Optical constants of homogeneous media in the linear response theory
Optical constants and Green's function of the electronic system
Quantum theory of band-to-band optical transitions and critical points
Indirect phonon-assisted transitions
Two-photon absorption
Exciton effects on the optical properties
Fano resonances and absorption lineshapes
Optical properties of vibronic systems
Optical properties of the Frank-Condon vibronic model
Optical properties of typical Jahn-Teller systems
Transitions rates at first and higher orders of perturbation theory
Further reading
Transport in intrinsic and homogeneously doped semiconductors
Fermi level and carrier density in intrinsic semiconductors
Impurity levels in semiconductors
Fermi level and carrier density in doped semiconductors
Thermionic emission in semiconductors
Non-equilibrium carrier distributions
Drift and diffusion currents
Generation and recombination of electron-hole pairs in semiconductors
Solutions of typical transport equations in uniformly doped semiconductors
Further reading
Transport in inhomogeneous semiconductors
Properties of the pn junction at equilibrium
Current-voltage characteristics of the pn junction
The bipolar junction transistor
The junction field-effect transistor (JFET)
Semiconductor heterojunctions
Metal-semiconductor contacts and MESFET transistor
The metal-oxide-semiconductor structure and MOSFET transistor
Further reading
Electron gas in magnetic fields
Magnetization and magnetic susceptibility
Energy levels and density-of-states of a free-electron gas in magnetic fields
Energy levels of the two-dimensional electron gas in magnetic fields
Energy levels of the three-dimensional electron gas in magnetic fields
Orbital magnetic susceptibility and de Haas-van Alphen effect
Orbital magnetic susceptibility of a two-dimensional electron gas
Orbital magnetic susceptibility of a three-dimensional electron gas
Spin paramagnetism of a free-electron gas
Magnetoresistivity and classical Hall effect
The quantum Hall effect
Free energy of an electron gas in a uniform magnetic field
Generalized orbital magnetic susceptibility of the free-electron gas
Further reading
Magnetic properties of localized systems and Kondo impurities
Quantum mechanical treatment of magnetic susceptibility
Magnetic susceptibility of closed-shell systems
Permanent magnetic dipoles in atoms or ions with partially filled shells
Paramagnetism of localized magnetic moments
Localized magnetic states in normal metals
Dilute magnetic alloys and the resistance minimum phenomenon
Some phenomenological aspects
The resistance minimum phenomenon
Microscopic origin of the Kondo interaction: a molecular model
Magnetic impurity in normal metals at very low temperatures
Further reading
Magnetic ordering in crystals
Ferromagnetism and the Weiss molecular field
Microscopic origin of the coupling between localized magnetic moments
Antiferromagnetism in the mean field approximation
Spin waves and magnons in ferromagnetic crystals
The Ising model with the transfer matrix method
The Ising model with the renormalization group theory
The Stoner-Hubbard itinerant electron model for magnetism
Further reading
Some phenomenological aspects of superconductors
The Cooper pair idea
Ground state for a superconductor in the BCS theory at zero temperature
Variational determination of the ground-state wavefunction
Ground-state energy and isotopic effect
Momentum distribution and coherence length
Excited states of superconductors at zero temperature
The Bogoliubov canonical transformation
Persistent currents in superconductors
Electron tunneling into superconductors
Treatment of superconductors at finite temperature and heat capacity
Diamagnetism of superconductors and Meissner effect
The phenomenological London model
Pippard electrodynamics and effective magnetic penetration depth
Macroscopic quantum phenomena
Order parameter in superconductors and Ginzburg-Landau theory
Magnetic flux quantization
Type-I and type-II superconductors
Cooper pair tunneling between superconductors and Josephson effects
The phonon-induced electron-electron interaction
Further reading
Subject index