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Zbl 1041.81100
Kennedy, Piers
The Woods-Saxon potential in the Dirac equation. (English)
[J] J. Phys. A, Math. Gen. 35, No. 3, 689-698 (2002). ISSN 0305-4470

Summary: 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.

MSC 2000:: *81U05 2-body potential scattering theory
35Q40 PDE from quantum mechanics

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Zentralblatt MATH Berlin [Germany]