Kennedy, Piers The Woods-Saxon potential in the Dirac equation. (English) Zbl 1041.81100 J. Phys. A, Math. Gen. 35, No. 3, 689-698 (2002). 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. Cited in 14 Documents MSC: 81U05 \(2\)-body potential quantum scattering theory 35Q40 PDEs in connection with quantum mechanics PDFBibTeX XMLCite \textit{P. Kennedy}, J. Phys. A, Math. Gen. 35, No. 3, 689--698 (2002; Zbl 1041.81100) Full Text: DOI arXiv