Fundamentals of solid-state materials

Fundamentals of electronic structure: the Schroedinger equation and its solution for free electrons, electrons in a potential well, and in a Coulomb potential. Variational principle and diagonalization. Electronic structure of molecules, and approximate solutations with linear combination of atomic orbitals. Hartree-Fock. Symmetry operation and their role in classifying eigenstates. Hamiltonian in a periodic potential and energy bands. Free-electron and tight-binding models. Fermi-Dirac statistics and distribution. Electrical transport and semiconductors. Optical properties of materials, and their quantum origin.