V-function method: to modeling trajectory-wave motion of an electron in a hydrogen-like atom

Valishin Nail Talgatovich, Smoylov Kirill Andreevich, Babina Sofia Vyacheslavovna

In this paper, the V-function method is considered as a possible apparatus for mathematical modeling of the trajectory-wave motion of an object (particle) in a Coulomb force field. The possibility of solving the direct and inverse problems of dynamics on the basis of this method is analyzed, in connection with which a study of the wave function for an object is carried out and its energy is determined. When modeling the motion of an electron in a Coulomb field, the method under consideration allows us to establish a rule for quantization of the energy of a hydrogen-like atom, which completely coincides with the classical results.

Keywords:trajectory-wave motion, motion modeling, wave function, wave equation, hydrogen-like atom.