Fermions in the background of mixed vector-scalar-pseudoscalar square potentials

TL;DR

This paper analyzes the Dirac equation with mixed vector, scalar, and pseudoscalar square potentials in 1+1 dimensions, revealing conditions for bound states and resonances, and mapping the problem to an effective Schrödinger equation.

Contribution

It introduces a comprehensive study of relativistic fermions in mixed potentials, deriving bound and resonant states, and establishing the role of pseudoscalar potential strength.

Findings

Resonant transmission coefficients exhibit oscillatory behavior.

Bound state energies match those of spinless particles in special cases.

Existence of bound states depends on the pseudoscalar potential's critical value.

Abstract

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 Schr\"{o}dinger 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.