The cylindrical \delta-potential and the Dirac equation
High Energy Physics - Phenomenology
2012-11-06 v3 Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1112.6402,
title = {The cylindrical \delta-potential and the Dirac equation},
author = {M. Loewe and F. Marquez and R. Zamora},
journal= {arXiv preprint arXiv:1112.6402},
year = {2012}
}
Comments
11 pages, 2 figures