Bound electron states in a charged chain within the Dirac description

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.