Computer‐aided evolution for solving the analytic Kronig‐Penny model

Abstract

The Kronig-Penney model consists of a periodic potential function, which is used to derive the concepts of allowed and forbidden energy bands. Here, to circumvent the tedious evolution, it is helpful to use computer methods to derive the textbook equation of the analytic Kronig-Penney model. The hierarchical methodology with the shorter symbols can effectively reduce the complication in the expression of the 4 × 4 matrix. By defining the symbol sequence, we can easily reduce terms by cancellation. With these methods and computer-aided evolution, we can derive the Kronig-Penney model from the matrix expression to the textbook form without the extremely laborious evolution.