RELATIVISTIC COULOMB PROBLEM FOR Z LARGER THAN 137

Abstract

We propose a relativistic one-parameter Hermitian theory for the Coulomb problem with an electric charge greater than 137. In the nonrelativistic limit, the theory becomes identical to the Schrödinger–Coulomb problem for all Z. Moreover, it agrees with the Dirac–Coulomb problem to order (αZ)2, where α is the fine structure constant. The vacuum in the theory is stable and does not suffer from the "charged vacuum" problem for all Z. Moreover, transition between positive and negative energy states could be eliminated. The relativistic bound states energy spectrum and corresponding spinor wave functions are obtained.