This course applies basic quantum mechanics principles (Schrödinger equation and perturbation theory) to derive the band structure theories of crystalline solids and understand the multiphysics nature of materials (including electrical, optical, optoelectronic, and topological properties). Topics in this course include single-particle Schrodinger equation and its application in several quantum mechanical systems; Dirac notation, non-degenerate and degenerate perturbation theories and their applications in hydrogen and helium atoms; classical free-electron gas model, quantum free-electron theory, quantum density of states, Fermi-Dirac distribution, Maxwell Boltzmann Distribution, Fermi energy, and Fermi surface; Bloch’s theorem, approaching band model through Schrödinger equation; nearly free-electron model, tight-binding model, Kronig-Penney model for deriving the formation of discrete energy levels and band structures of crystalline solids; apply band structures to classify materials and understand electrical, optical, and topological properties of recently emerging materials systems (two-dimensional materials and topological insulators etc.).