Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential
High Energy Physics - Theory
2009-10-06 v1 Quantum Physics
Abstract
Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schr\"{o}dinger-like equation with an effective Rosen-Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and more efficient problem of solving an irrational algebraic equation.
Keywords
Cite
@article{arxiv.0906.0342,
title = {Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential},
author = {M. G. Garcia and A. S. de Castro},
journal= {arXiv preprint arXiv:0906.0342},
year = {2009}
}