More stringent confinement limit of the Dirac particle in one dimension

Abstract

Unanyan, Otterbach, and Fleischhauer [Phys. Rev. A 79, 044101 (2009)] found that the confinement limit of a one-dimensional Dirac particle in a symmetric potential is half its corresponding Compton length and can be derived from the Dirac equation. Then, Toyama and Nogami [Phys. Rev. A 81, 044106 (2010)] conjectured that a more stringent limit holds for any symmetric potential. I would like to show, in this Brief Report, that the confinement limit conjectured by Toyama and Nogami can be derived from the Dirac equation.