The cylindrical δ-potential and the Dirac equation

Details The cylindrical δ-potential and the Dirac equation The cylindrical δ-potential and the Dirac equation

2011-12-29

arxiv.org/abs/1112.6402v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

11 pages, 2 figures

Scientific paper

In this article we discuss the Dirac equation in the presence of an attractive cylindrical \delta-shell potential V(\rho)=-a\delta(\rho-\rho_0) , where \rho is the radial coordinate and a>0. We present a detailed discussion on the boundary conditions the wave function has to satisfy when crossing the support of the potential, proceeding then to explore the dependence of the ground state on the parameter a, analyzing the occurrence of supercritical effects. We also apply the Foldy-Wouthuysen transformation, discussing the non-relativistic limit of this problem.

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