On the Influence of the Unit Cell Type on the Wave Function in One-Dimensional Kronig-Penney Models

Abstract

We study the influence of the different choice of unit cells on the Bloch solutions of Schrçdinger equation for one-dimensional periodic Kronig- Penney models with rectangular potential barriers or potential wells and partially constant effectiv mass. We obtain generalized Kronig-Penney relations for bulk states and exact expressions for the corresponding periodic parts of the Bloch wave functions for the two possible choices of the matching conditions in an unit cell. We show also that our analitic expressions reduce to the well known expressions for the Kronig-Penney relations and Bloch waves under constant effective mass and appropriate matching conditions.