Dirac Equation with Coupling to 1/r Singular Vector Potentials for all Angular Momenta

Foundations of Physics 40 (8):1088-1095 (2010)
Abstract
We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r 2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and Eckart potentials
Keywords Dirac equation  Singular potentials  Non-zero angular momentum  Energy spectrum  Hulthén  Eckart
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DOI 10.1007/s10701-010-9431-5
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