Dirac Equation in the Field of a Charged Cosmic String and in the Field of a Point Charge with Z > 137

Abstract

In both spherical and cylindrical coordinates, the radial Dirac equation can be written in the form of a Schrodinger equation with an effective potential. It is shown that the difficulties at r -+ 0 for the Dirac equation in the field of a point charge for Z > 137 are the same as those for the Schrodinger equation with a l/r2 potential. The effective potential is used to show that similar difficulties do not arise for the field of a line charge, so allowing the consideration of the motion of electrons in the field of a charged superconducting cosmic string without considering the internal structure of the string.