Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation

TL;DR

This paper investigates one-dimensional PT-symmetric potentials in the Dirac equation, demonstrating conditions for real spectra and reflectionless scattering, including non-vanishing asymptotic potentials, thus advancing understanding of PT-symmetric quantum systems.

Contribution

It introduces conditions under which PT-symmetric Dirac potentials are reflectionless and have real spectra, even when potentials do not vanish at infinity.

Findings

Bound-state spectra are real under specified conditions.

Potentials are reflectionless and conserve unitarity.

Reflectionless properties extend to non-vanishing asymptotic potentials.

Abstract

We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are real and the potentials are reflectionless and conserve unitarity in the scattering process. Absence of reflection makes it meaningful to consider also PT-symmetric potentials that do not vanish asymptotically.