X-ray scattering and crystalline structure. Numerical estimate of thermal
atomic fluctuations. Elastic scattering from a single atom. Form factor. Bragg
condition. Momentum transfer. Scattering from many atoms. Lattice sums. Superlattices. Reciprocal lattice. Miller indices. Experimental
methods of X-ray diffraction: von~Laue method, powder method. X-ray production:
Brehmsstrahlung, synchroton radiation. Correlation functions. Long-range
(positional) order. Radial correlation functions. Liquids. Other phases of
condensed matter. Quasicrystals. Bravais
lattice. Point groups. Schoenflies notation. Wigner-Seitz cell. Examples.
Coordination number: the problem of close packing. Reciprocal lattice. Lattices
with basis. Brillouin zone. Electronic structure of solids. Free electron
model. Born-von~K\'arm\'an boundary conditions. Alkali metals. Ground state:
the Fermi sea. Fermi energy and electron density. Wigner-Seitz radius. Lattice
sums and continuum (long-wavelength) limit. Some results for
reduced-dimensional systems. Density of
states. Statistical mechanics of non-interacting fermions. Fermi distribution.
Chemical potential. Sommerfeld expansion. Electronic specific heat. Non-interacting
electrons in a periodic external potential. Bloch theorem. Crystal momentum. Density of states for Bloch
electrons. Electronic Topological Transitions and Van~Hove singularities. Weakly
bound electrons. Diffraction of Bloch electrons at Bragg planes. Brillouin
zones. Dispersion relation plots along symmetry contours. Fermi surface. Harrison construction. Tight-binding model. Linear
Combination of Atomic Orbitals. Example: tight-binding dispersion relation for
a square lattice. Relevance for the high-T_c cuprates. Example: tight-binding dispersion relation for
a honeycomb lattice. Relevance for graphene. Electron-electron interaction.
Hartree and Hartree-Fock equations. Second quantization. Derivation of the
Hartree-Fock equations. Exchange energy. Jellium model. Lindhard function.
Exchange hole. Screening. Thomas-Fermi theory. Thomas-Fermi equation for the
inhomogeneous electron density in a hydrogenic atom or ion. Density Functional
Theory. Kohn-Hohenberg theorem. LDA and GGA approximations. Stability of
matter. Lattice vibrations. Harmonic approximation. Normal modes. Example:
harmonic linear chain. Acoustic branch. Optical branch. Hamiltonian for
harmonic lattice vibrations: first quantization. Hamiltonian for harmonic
lattice vibrations: second quantization. Phonons. Phonon specific heat.
Einstein model. Debye model. Realistic phonon density of states. Effects of
anharmonicity.


































































































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