Quantum mechanics in theK-field formalism: Kepler's problem for spin particles

Abstract

Using the well-known Kepler's problem, an attempt is made to demonstrate a procedure for constructing a nonrelativistic approximation of a quantum-mechanical model for steady states of hydrogen atoms in the K-field formalism. In this model, an electron is assumed to possess an intrinsic moment (spin) which, according to Frenkel, is comparable to the magnetic moment. It is shown that Lyapunov-stable trajectories of the K-particle (a test point particle representing the classical model of an electron in an atom) correspond to the conventional steady states of hydrogen atoms, with the trajectories being similar to those in the spin-zero particle model. The proposed model of the electronic structure in a hydrogen atom provides an insight into the physical cause of the atomic superfine structure and the physical meaning of the constant α=c/mc.