Stationary states of spinless particles in square potentials

TL;DR

This paper investigates relativistic scattering and bound states of spinless particles in square potentials, revealing novel phenomena like antiparticle-mediated scattering and the suppression of the Schiff-Snyder-Weinberg effect due to scalar coupling.

Contribution

It provides a comprehensive analysis of the Klein-Gordon equation with mixed potentials, uncovering new relativistic effects not predicted by nonrelativistic quantum mechanics.

Findings

Antiparticle bound states mediate anomalous scattering.

Scalar coupling inhibits the Schiff-Snyder-Weinberg effect.

Relativistic effects differ significantly from nonrelativistic predictions.

Abstract

The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis and calculation of the reflection and transmission coefficients for the scattering of particles in a square potential, with an arbitrary mixing of vector and scalar couplings, reveal circumstances which conflict with the predictions from nonrelativistic quantum mechanics. It is shown that such anomalous scatterings are mediated by antiparticle bound states, even if the incident particles have low energies. The analysis of bound states also reveals surprising results, remarkable is the inhibition of the Schiff-Snyder-Weinberg effect due to the presence of a scalar coupling.