The magnetic vector potential, Klein-Gordon equation and Klein’s paradox in relativistic quantum mechanics

Abstract

This thesis evaluates solutions to the Klein-Gordon equation with scalar and vector potentials in the Symmetric and Landau gauges. The solution for the Klein-Gordon equation in the Symmetric gauge does reproduce elements of the two dimensional quantum harmonic oscillator. The Landau gauge solution is used in the velocity selector situation where particles can have acceleration free motion for a selected velocity. The Klein Paradox for spin less particles is reviewed and its application to the Klein- Gordon equation shows that the vector potential can have an effect on particle pair production without the violation of conservation of momentum or energy, that this effect is to suppress the particle pair production associated with Klein’s paradox and that the suppressive effect can, under certain conditions, become strong enough to prevent particle pair production in Klein’s paradox when the scalar potential is otherwise many times what would be necessary to create Klein’s paradox particle pairs.