Fine Structure of the Atomic Hydrogen Spectrum in the Lobachevsky Space

Abstract

Solutions of the radial Dirac equation for a particle with spin 1/2 moving in the Coulomb field in the Lobachevsky space are presented in the form of power series. The three-term recurrence relations for the coefficients of the series are obtained and used to derive the expansions in inverse powers of the radius of curvature for the energy levels of bound states of the particle.