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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