Scattering of relativistic spinless particles within the Feshbach-Villars formalism

• Published in: Heliyon Vol. 8; no. 10; p. e11215
• Main Authors: Chargui, Y., Dhahbi, A., Karam, A.R.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-10-2022; Elsevier
• Subjects: Feshbach Villars formalism; One-dimensional scattering; Partial-wave decomposition; Relativistic spinless particles; Scattering matrix; Relativistic spinless particles; One-dimensional scattering; Scattering matrix; Feshbach Villars formalism; Partial-wave decomposition
• ISSN: 2405-8440; 2405-8440
• DOI: 10.1016/j.heliyon.2022.e11215

We consider the relativistic quantum scattering of spinless particles in one-spatial dimension using the Feshbach-Villars formalism. We construct the general form of the scattering matrix, for symmetric and non-symmetric potentials, based on the symmetry properties of the Feshbach-Villars equation. Then, since in one dimension there are only two partial waves associated with even and odd parities, we show, in a simple and comprehensive way, how to describe this transmission-reflection problem using partial-wave decomposition. As an illustration, we also discuss the special case of scattering by a symmetric square-well potential.
One-dimensional scattering; Relativistic spinless particles; Feshbach Villars formalism; Scattering matrix; Partial-wave decomposition