Exact solutions for a charged particle in a uniform electric field with alternating site energies: perturbation theory

Abstract

The energy spectrum and the eigenvectors of a charged particle in a uniform electric field with alternating site energies are studied for infinite systems. For the case of large energy mismatch, exact solutions are presented by using perturbation theory, from which it is found that the spectrum is that of two interspaced Stark ladders. The character of these Stark ladders is that the difference of the ratio of the energy and the field between two energies on a same rung is an even number.