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The Woods-Saxon Potential in the Dirac Equation

P. Kennedy
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Abstract

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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P. Kennedy. 2001-07-20. The Woods-Saxon Potential in the Dirac Equation. https://doi.org/10.1088/0305-4470%2F35%2F3%2F314

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