Analytical solutions of the Dirac equation with a scalar linear potential

Abstract

The Dirac equation with a scalar linear potential is solved analytically. Analytical solutions are shown to exist when there are some quantitative relations between the strength constant of the linear potential and the mass of the particle. The analytical solutions are assumed to be of asymptotic form times a polynomial expression for the radial coordinate r. Actual solutions are found up to the order of r5. © 2013 © 2013 Author(s).