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arXiv · 0906.0342

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

M. G. Garcia·A. S. de Castro
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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 Schrödinger-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.

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M. G. Garcia, A. S. de Castro. 2009-06-01. Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential. https://doi.org/10.1016/j.aop.2009.05.010

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