Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances

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AYDOĞDU O., Arda A., Sever R.

JOURNAL OF MATHEMATICAL PHYSICS, vol.53, no.4, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 4
  • Publication Date: 2012
  • Doi Number: 10.1063/1.4705284
  • Journal Name: JOURNAL OF MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Middle East Technical University Affiliated: Yes

Abstract

Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are calculated by using behavior of the wave functions at infinity. The same analysis is done for the constant mass case. It is also pointed out that our results are in agreement with those obtained in literature. Meanwhile, an analytic expression is obtained for the transmission resonance and it is observed that the expressions for bound states and resonances are equal for the energy values E = +/- m. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705284]