Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric 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.

arXiv comment52 pages, 14 figures, 2 tables

References in corpus (20)

• Electronic States of Graphene Nanoribbons
• The transfer matrix: a geometrical perspective
• Four-Parameter Point-Interaction in 1-D Quantum Systems
• The Friedrichs Model and its use in resonance phenomena
• Two-point one-dimensional $\delta$-${\delta }^{\prime }$ interactions: non-abelian addition law and decoupling limit
• The regulated four parameter one dimensional point interaction
• Distribution theory for Schrödinger's integral equation
• One-Dimensional Semirelativistic Hamiltonian with Multiple Dirac Delta Potentials
• Distributional approach to point interactions in one-dimensional quantum mechanics
• One-dimensional scattering of fermions on $\delta$-impurities
• Dynamical Casimir effect with $\delta -{\delta }^{\prime }$ mirrors
• Exact spectral function of a Tonks-Girardeau gas in a lattice
• Two-dimensional Dirac operators with general $\delta$-shell interactions supported on a straight line
• Effects of Two Successive Parity-Invariant Point Interactions on One-Dimensional Quantum Transmission: Resonance Conditions for the Parameter Space
• Casimir effect for Dirac lattices
• The Solution of the Relativistic Schrodinger Equation for the ${\delta }^{\prime }$-Function Potential in 1-dimension Using Cutoff Regularization
• Resonant Transmission in One-Dimensional Quantum Mechanics with Two Independent Point Interactions: Full Parameter Analysis
• Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal ${\delta }^{\prime }$ interactions
• Massive and massless two-dimensional Dirac particles in electric quantum dots
• Bound states of a one-dimensional Dirac equation with multiple delta-potentials