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Atomic vibrations are expressed in terms of bosonic fields (phonons), while electrons form a Fermi liquid embedeed in the periodic potential of nuclei. From these fields we evaluate elementary properties of crystals.
Last update: T_FUUK (24.05.2004)
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Introduction to the theory of solid state Last update: LIPAVSKY/MFF.CUNI.CZ (15.05.2008)
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examination Last update: Lipavský Pavel, prof., CSc. (30.10.2019)
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CH. Kittel: Introduction to Solid State Physics. (1963), český překlad: Úvod do fyziky pevých látek
J. Celý: Kvazičástice v pevných látkách, SNTL, Praha (1977). Last update: LIPAVSKY/MFF.CUNI.CZ (15.05.2008)
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chalk talks Last update: LIPAVSKY/MFF.CUNI.CZ (15.05.2008)
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Required skills: basic formulation of Hamiltonian, adiabatic approximation, Hellmann-Feynman theorem, harmonic approximation, phonon dispersion bands, Brillouin zone, Born-Karman boundary condicions, specific heat of phonons, neutron difraction on crystal, Mössbauer effect, relativistic corrections to Schrödinger equation, Bloch theorem, electron band structure, Kan model, density of states, specific heat of electrons, Pauli spin paramagnetizm, Laundau orbital diamagnetizm, de Haas-van Alphen effect, Peierls instability. Last update: Lipavský Pavel, prof., CSc. (30.10.2019)
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In order to describe vibrations of atoms we introduce such basic concepts of solids as the Brillouine zone, Born-Karman boundary conditions or energy dispersion bands. Within the second quantisation we evaluate for instance the phonon specific heat, the neutron diffraction and the Mössbauer effect. Within the approximation of free electrons we evaluate the electronic specific heat, spin and orbital magnetic susceptibilities, de Haas-van Alphen effect and cyclotron resonance. For electrons in real crystals we derive electronic energy bands from the Bloch theorem. Using Kane and Kronig-Penney models we explain the origin and meaning of specific featuers of these bands. Within the second quantisation we introduce a filling of bands which is responsible for a distinction between metals and isolators. A competition of physical processes leading to these two types of crystals is demonstrated on the Peierls transition. Effects of an electro-electron interaction we demonstrate on the superconductivity. After a phenomenological introduction involving the thermodynamic description, the two-fluid model, the London's theory and the Ginzbur-Landau theory, we derive some properties from the microscopic model of Bardeen, Cooper and Schrieffer. A systematic theory of interacting electrons we introduce only for the zero temperature. We derive Feynman diagrams for the Coulomb interaction. We evaluate the polarization operator, from which we obtain the screening and the plasma oscillation. Last update: T_FUUK (24.05.2004)
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quantum mechanics, basics of the quantum statistics Last update: LIPAVSKY/MFF.CUNI.CZ (15.05.2008)
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