A Nonrelativistic Approximation for Energy Spectrum of a Vector Particle with Anomalous Magnetic Moment in the Coulomb Field

Recently, transition to the nonrelativistic limit was performed for the simplified description of a vector particle with anomalous magnetic moment in the Coulomb field. The problem was reduced to a single radial second order equation in the case of a minimal value of the total angular momentum. However, the exact energy spectrum was not obtained. In the present paper, the quantization rule within the framework of the WKB approximation modified by Langer is used. This approximation gives the exact expression for the energy in the Coulomb problem without anomalous magnetic moment. The dependence of discrete energy levels on anomalous magnetic moment is presented.