Scattering of neutral fermions by a pseudoscalar potential step in two-dimensional space-time

TL;DR

This paper investigates how neutral fermions scatter off a pseudoscalar potential step in 2D space-time, revealing unexpected solution behaviors, resolving an uncertainty paradox, and suggesting possible bound states.

Contribution

It introduces new insights into scattering phenomena and bound states of neutral fermions in pseudoscalar potentials, extending previous theoretical understanding.

Findings

Identifies unexpected aspects of scattering solutions beyond Klein's paradox.

Resolves an uncertainty principle paradox using effective Compton wavelength.

Provides plausibility for bound-state solutions in pseudoscalar double-step potentials.

Abstract

The problem of scattering of neutral fermions in two-dimensional space-time is approached with a pseudoscalar potential step in the Dirac equation. Some unexpected aspects of the solutions beyond the absence of Klein\'{}s paradox are presented. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength. Added plausibility for the existence of bound-state solutions in a pseudoscalar double-step potential found in a recent Letter is given.