ORIGINAL RESEARCH article
Front. Phys.
Sec. Quantum Engineering and Technology
This article is part of the Research TopicRecent Mathematical and Theoretical Progress in Quantum MechanicsView all 9 articles
Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric Two Point Interactions
Provisionally accepted
- 1Independent Researcher, Ponta Grossa, Brazil
- 2Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, Valladolid, Spain
- 3Department of Mathematics & Statistics, Universidade Estadual de Ponta Grossa, Ponta Grossa, Paraná, Brazil
- 4Department of Physics, Concordia College, Moorhead, United States
Select one of your emails
You have multiple emails registered with Frontiers:
Notify me on publication
Please enter your email address:
If you already have an account, please login
You don't have a Frontiers account ? You can register here
We consider the one-dimensional Dirac equation with the most general relativistic contact interaction supported on two points symmetrically located with respect to the origin. In order to determine the shape of the interaction, we use a distributional method, which in the present case is equivalent to the standard method of defining contact interactions by self-adjoint extensions of symmetric operators. The interaction on each of these two points depends on four parameters, each one having a clear physical meaning. We are interested in the scattering and confining properties of this model. We focus our attention on even or odd interactions under parity transformations and investigate the existence of critical and supercritical states, bound states, confinement and scattering resonances for some particular interactions of special interest.
Keywords: Bound states energies, Confining properties, One-dimensional Dirac equation, Parity-symmetric interactions, point interactions, Resonances, Schwartz distributions
Received: 27 Dec 2025; Accepted: 13 Feb 2026.
Copyright: © 2026 Bonin, Gadella, Lunardi and Manzoni. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: José Tadeu Lunardi
Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.