Generalization of Schrödinger Equation for Band Theory and Inelastic Scattering Problems

Abstract

In this work ordinary Schrödinger equation (OSE) is generalized by using the expression for the electromagnetic wave expression inside a medium, instead of the in free space for the OSE. This generalized Schrödinger equation ( GSE) is strongly dependent on the properties of the medium, such as electric and magnetic susceptibility as well as particle density and frictions, which are apparent through the conductivity which depends on the particle density and the relaxation time which is related to the friction. Thus GSE is unlike OSE which does not depends on the properties of the medium. This generalized version is utilized to explain the formation of energy band in solids as well as the inelastic scattering by using well-known parameters like conductivity, electric susceptibility and magnetic susceptibility. Therefore, this model is better than existing models, which use unknown parameter to explain these phenomena. The solution of these models is simple and overlaps with some experimental observations. This model also refers to most of the existing band structures and inelastic scattering models.