The Woods-Saxon Potential in the Dirac Equation

Details The Woods-Saxon Potential in the Dirac Equation The Woods-Saxon Potential in the Dirac Equation

2001-07-20

arxiv.org/abs/hep-th/0107170v1

J.Phys.A35:689-698,2002

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, 4 figures. Submitted to JPhysA

Scientific paper

10.1088/0305-4470/35/3/314

The two-component approach to the one-dimensional Dirac equation is applied to the Woods-Saxon potential. The scattering and bound state solutions are derived and the conditions for a transmission resonance (when the transmission coefficient is unity) and supercriticality (when the particle bound state is at E=-m) are then derived. The square potential limit is discussed. The recent result that a finite-range symmetric potential barrier will have a transmission resonance of zero-momentum when the corresponding well supports a half-bound state at E=-m is demonstrated.

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