Paraxial wave function and Gouy phase for a relativistic electron in a uniform magnetic field

Abstract

A connection between relativistic quantum mechanics in the Foldy-Wouthuysen representation and the paraxial equations is established for a Dirac particle in external fields. The paraxial form of the Landau eigenfunction for a relativistic electron in a uniform magnetic field is determined. The obtained wave function contains the Gouy phase and significantly approaches to the paraxial wave function for a free electron.