Effective-Mass Dirac Equation for Woods-Saxon Potential: Scattering, Bound States and Resonances

2012/04/30 by Oktay Aydoğdu, Altug Arda, Ramazan Sever · 1 citation
Physics and Astronomy · Mathematics · #math-ph #hep-ph #math.MP #quant-ph

paper · pdf · doi:10.1063/1.4705284

published as J. Math. Phys. 53, 042106 (2012) · 20 pages, 6 figures

arxiv created 2012/04/30 · arxiv updated 2012/05/01

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 observed that the expressions for bound states and resonances are equal for the energy values E=± m.

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