The quantum mechanics of electric conduction in crystals

We introduce a model of electrons incident on a one-dimensional periodic potential and show that conduction is a result of the interference of different parts of an electron wave that bounce multiple times through a series of potentials, ultimately being transmitted or reflected. Simple iterative equations are derived that determine the transmission and reflection coefficients of a periodic system. We find that total reflection of the electron occurs in certain energy ranges, as well as ranges of energy within which complete transmission can occur. The energy ranges in which transmission occurs are equivalent to the conduction bands traditionally found using Bloch's theorem. These equations are solved numerically, allowing a concrete demonstration of conduction. The disordered case is also addressed. ©2010 American Association of Physics Teachers