Electron Propagation in Periodic Potentials

Sammanfattning: In this bachelor thesis we study the propagation of electrons in crystals. The crystalline structure is modeled as a one dimensional periodic potential primarily composed of delta function potential barriers. We use two different models to describe how a particle behaves in such a periodic structure. The first model is the Kronig Penney model described by S. Gasiorowicz in [ 1]. The second model is described by Olsen and Vignale in the article "The Quantum mechanics of electric conduction in crystals" [ 3]. We show that there exists certain ranges of energy for which electron propagation can occur, namely the allowed energy bands separeted by regions of forbidden energies. In addition, we solve the Schrödinger equation numerically for some simple cases and reproduce some of the results seen from the two mentioned models.