The linear potential and the Dirac equation

Abstract

The solution of the Dirac equation for an attractive linear potential is considered. The Lorentz nature of the potential (vector or scalar) affects the existence of bound states. For simplicity, and since it is sufficient for the goals of this study, only the ground state is considered. The case of equal vector and scalar pieces of the linear potential is emphasized because it lends itself to a simple analytic solution. This solution corresponds to a state which is strictly bound. For a linear potential with a larger component of the vector part, we find a state that is only quasi-bound, but its decay can be strongly inhibited by an effective potential barrier.