2015/07/31 by Luiz P. de Oliveira, Luis B. Castro
Physics and Astronomy · Mathematics · #quant-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.aop.2015.10.018
published as Ann. Phys. (N.Y) 364 (2015) 99 · 10 pages, 5 figures. arXiv admin note: text overlap with arXiv:nucl-th/0604068 by other authors
arxiv created 2015/11/04 · arxiv updated 2015/11/24
The general Dirac equation in 1+1 dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector-scalar-pseudoscalar square potentials, the states of relativistic fermions are investigated. This relativistic problem can be mapped into a effective Schrödinger equation for a square potential with repulsive and attractive delta-functions situated at the borders. An oscillatory transmission coefficient is found and resonant state energies are obtained. In a special case, the same bound energy spectrum for spinless particles is obtained, confirming the predictions of literature. We showed that existence of bound-state solutions are conditioned by the intensity of the pseudoscalar potential, which posses a critical value.