Reflectionless PT-Symmetric Potentials in the One-dimensional Dirac Equation

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