A new approach to discrete Schrodinger equations with external field: DC electric field

Abstract

For continuous Schrodinger equations the discretization process is defined by preserving the Heisenberg equation of motion rather than the Schrodinger equation itself. For instance, strong changes are obtained for one particle in DC electric fields. In the old discretization process, all eigenstates are factorially localized and the spectrum becomes discrete. On the other hand, in the model, the author conjectured that the spectrum becomes continuous. The author remarks that discrete systems play an important role in physics because they are, in many cases, a first approach to real systems. The goal is to study the equivalence between continuous and discrete Schrodinger equations by preserving the Heisenberg equations of motion.