Solution of the Schrodinger Equation for Periodic Potentials using Kronig Penney Model.

Abstract

This project presents a detailed working of solutions to the Schrodinger equation for periodic potentials using the Kronig Penney model. Periodic potentials are a fundamental frame work of quantum mechanics with significant applications to solid state physics and nuclear physics among others. Utilizing Bloch theorem, we derive the energy eigen states and the corresponding wave functions for particles subjected to a periodic potential. Furthermore, we explore the implications of theses solutions based on band structure formation clearly illustrating the emergence of allowed energy bands within a crystal lattice. The results not only enhance our understanding of the fundamental quantum mechanics but also paves the way for future developments in technology reliant on quantum phenomena such as quantum computing and semi conductor devices.