paper

Solution of the relativistic Dirac-Hulthen problem

arXiv:hep-th/0405022 · doi:10.1088/0305-4470/37/22/007

Abstract

The one-particle three-dimensional Dirac equation with spherical symmetry is solved for the Hulthen potential. The s-wave relativistic energy spectrum and two-component spinor wavefunctions are obtained analytically. Conforming to the standard feature of the relativistic problem, the solution space splits into two distinct subspaces depending on the sign of a fundamental parameter in the problem. Unique and interesting properties of the energy spectrum are pointed out and illustrated graphically for several values of the physical parameters. The square integrable two-component wavefunctions are written in terms of the Jacobi polynomials. The nonrelativistic limit reproduces the well-known nonrelativistic energy spectrum and results in Schrodinger equation with a "generalized" three-parameter Hulthen potential, which is the sum of the original Hulthen potential and its square.

13 pages, 3 color figures

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