# Pair states in one-dimensional Dirac systems

## TL;DR

This paper provides analytic solutions for two-body Dirac systems in one dimension with a smooth square well potential, exploring bound states, including within the gap, relevant for excitons in carbon nanotubes.

## Contribution

It introduces exact solutions for the relativistic two-body problem in 1D with a smooth potential, including the delta interaction limit and bound states within the gap.

## Key findings

- Analytic solutions for stationary and moving pairs in 1D Dirac systems.
- Existence of bound states within the energy gap for same-charge particles.
- Insights applicable to excitonic states in narrow-gap carbon nanotubes.

## Abstract

Analytic solutions of the quantum relativistic two-body problem are obtained for an interaction potential modeled as a one-dimensional smooth square well. Both stationary and moving pairs are considered and the limit of the {\delta}-function interaction is studied in depth. Our result can be utilized for understanding excitonic states in narrow-gap carbon nanotubes. We also show the existence of bound states within the gap for a pair of particles of the same charge.