Geometrization for a quantum-mechanical problem of the spin 1 particle with anomalous magnetic moment in the Coulomb field

Abstract

In [1] the quantum-mechanical problem for a spin 1 particles with anomalous magnetic in the presence of external Coulomb field was studied and the system of radial equations was obtained. It was shown that the system cannot be solved completely even in the case of ordinary particle without additional electromagnetic moments. To simplify the problem, restriction to non-relativistic equations was performed and the system of two 4-th order ordinary differential equations was found out. Its Frobenius solutions were constructed and transcendental solutions and corresponding energy spectra were found. However, the problem cannot be considered as studied exhaustively. In this study the problem of spin 1 particle with anomalous magnetic moment in the external Coulomb field are considered in non-relativistic approximation using Kosambi–Cartan–Chern geometrical approach (KCC-theory) [2].