Fractional Angular Momenta, Gouy and Berry phases in Relativistic Bateman-Hillion-Gaussian Beams of Electrons

Robert J. Ducharme, Irismar Gonçalves da Paz, Armen G. Hayrapetyan

A new Bateman-Hillion solution to the Dirac equation for a relativistic Gaussian electron beam taking explicit account of the $4$-position of the beam waist is presented. This solu…