Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric Two Point Interactions

TL;DR

This paper analyzes the scattering and bound state properties of a one-dimensional Dirac equation with general two-point contact interactions, exploring parity effects and resonance phenomena.

Contribution

It introduces a distributional method to characterize relativistic contact interactions with four parameters and studies their physical implications in bound and scattering states.

Findings

Identified conditions for bound and resonance states in the model.

Analyzed the impact of parity symmetry on interaction properties.

Explored critical and supercritical states in the context of two-point interactions.

Abstract

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.