Bound electron states in a charged chain within the Dirac description

TL;DR

This paper derives exact analytical solutions for bound electron states in a charged ion chain using the Dirac equation, revealing natural spin coupling effects without additional assumptions.

Contribution

It introduces a new spinor invariant and provides the first exact three-dimensional solutions for electrons in a charged chain within the Dirac framework.

Findings

Exact analytical expressions for bound states are obtained.

Electron spin coupling arises naturally from the Dirac equation.

The approach eliminates the need for artificial spin-orbit interaction terms.

Abstract

For the first time the exact analytical expressions for the three-dimensional bound electron states in the Coulomb field of the chain consisting of positively charged ions, are obtained within the Dirac description, using the new spinor invariant found for this problem. It is demonstrated that within such approach the coupling between electron spin and its one-dimensional propagation along the chain naturally arise, without any need to include artificially into the equations the so-called spin-orbit interaction.