Lecture 09: Bloch's Theorem
Have you ever wondered how electrons can sneak through a metal and conduct electricity with all those atoms in the way? It's Bloch's theorem. The electrons organize themselves into the right quantum mechanical states that automatically take into account the periodicity of the crystal. Electrons in a metal are shared by each atom in a type of molecular bond that extends over the whole crystal. These are the states which carry current. This lecture is heavy on the quantum mechanics -- you'll hear about eigenstates and eigenvalues, and how in a crystal, the eigenstates of energy can be simultaneously diagonalized with the eigenstates of translation in the crystal. These give the states mentioned above, where the electrons are delocalized throughout the whole crystal.