An Algebraic approach to the band structure of periodic potentials

ABSTRACT AN ALGEBRAIC APPROACH TO THE BAND STRUCTURE OF PERIODIC POTENTIALS OL?AR, Eser M.Sc, Engineering Physics Department Supervisor: Assists. Prof. Dr. Ramazan KOÇ January 2002, 63 pages A general method based on Lie algebra with three generators is proposed in order to successfully produce physically significant periodic potentials. Some potentials in one dimension are solved in algebraic framework using the Lie algebra. A novel Kronig-Penney model is developed to obtain energy band structure of Kronig-Penney type and Hyperbolic periodic potentials. Our approach can be applied to the other periodic systems with some modifications. In addition, generalized Kronig-Penney model is formulated in one dimension for contact interactions. Here, eigenvalue equations are obtained by using transfer matrix formalism. It has been shown that the method given in this thesis is useful to generate periodic quasi-exactly solvable potentials and to clarify their band structure. The algebraic method presented here leads to a number of physical potentials given in the literature. TC YÛKSEKÖÖRTTIM KDB0UT DOKÜMANTASYON Key words: Periodic potentials, Kronig-Penney model, contact interaction, Lie algebra. m