Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric Two Point Interactions
Carlos A. Bonin, Manuel Gadella, José T. Lunardi, Luiz A. Manzoni
TLDR
Analyzes bound states, resonances, and confinement in a 1D Dirac equation with parity-symmetric two-point relativistic contact interactions.
Key contributions
- Investigates the 1D Dirac equation with general relativistic contact interactions at two symmetric points.
- Defines interactions using a distributional method, equivalent to self-adjoint extensions.
- Examines critical/supercritical states, bound states, confinement, and scattering resonances.
- Focuses on even/odd interactions under parity transformations for specific cases.
Why it matters
This paper provides a detailed analysis of relativistic quantum systems with localized interactions, crucial for understanding particle behavior in confined spaces. Its findings on bound states and resonances contribute to quantum field theory and condensed matter physics.
Original 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.
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