Bound electron states in a charged chain within the Dirac description

Abstract

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