Abstract: The technique of beam optics is applied to the description of the wave function of Dirac electrons. This approach is illustrated by considering electron transmission through simple nonhomogeneous structures, such as flat and bent p-n junctions and superlattices. We found that a convex p-n junction compresses the beam waist, while a concave interface widens it without loosing its focusing properties. At a flat p-n junction the waist of the transmitted Gaussian beam can be narrowed or widened, depending on the angle of incidence. A general condition is derived for the occurrence of beam collimation in a superlattice which is less stringent than previous discussed.

Abstract: The ordering of N equally charged particles (-e) moving in two dimensions and confined by a Coulomb potential, resulting from a displaced positive charge Ze is discussed. This is a classical model system for atoms. We obtain the configurations of charged particles which, depending on the value of N and Z, may result in ring structures, hexagonal-type configurations, and for N/Z approximate to 1 in an inner structure of particles which is separated by an outer ring of particles. For N/Z << 1, the Hamiltonian of the parabolic confinement case is recovered. For N/Z approximate to 1, the configurations are very different from those found in the case of a parabolic confinement potential. A hydrodynamic analysis is presented in order to highlight the correlations effects.