Abstract
The difficulties associated with application of the shifted large-N technique to the Dirac equation have been resolved by applying the method to the Klein-Gordon equation in which a spin-orbit interaction term is included analogous to Pauli theory. Explicit analytical expressions for the relativistic screened Coulomb bound-state energies, radial wave functions, and normalizations are given. For the point-Coulomb problem, we restore exact results for the relativistic binding energies and almost exact wave functions. The 1/N expansion results are then compared with the exact numerical solutions as well as with those obtained in other analytical methods for a number of screened Coulomb potentials and for a wide range of atomic numbers Z. In general, excellent agreement is found. In contrast to the limited applicability of the usual perturbative methods, our technique is found to be flexible and may be extended to a more general class of relativistic potentials that has applications in atomic and quarkonium physics. Encouraging aspects of the present approach are also briefly discussed.
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