Eastern-European Journal of Enterprise Technologies

A method of V-function: ultimate solution to the direct and inverse problems of dynamics for a hydrogen-like atom

N T Valishin, Sergey A. Moiseev

Published Aug 30, 2017• 3 citations

Abstract

Based on the method of V-function, a continuation of the optical-mechanical analogy is attained. In contrast to classic quantum mechanics, a trajectory-wave motion of the particle is explored. We highlight the presence of energy quantization of the particle and the availability of solution without a particle in the case of rectilinear uniform motion at constant speed. A solution to the direct and inverse problems of dynamics is searched for in a new statement for a hydrogen-like atom. When solving a direct problem, we find a stationary wave function of the electron in a hydrogen-like atom, with its properties investigated. When searching for a final solution to the stationary wave equation, we take into account a solution to the inverse problem of dynamics for the electron. A linear dependence between two particular solutions is shown. The second linearly independent solution is found, decaying exponentially to zero. We present charts of the stationary solution for a wave of the particle (electron) for three lower stationary states. Energy levels of a hydrogen-like atom are determined as a solution to the inverse problem of dynamics, which fully coincide with the classical results by Schrödinger and Bohr. A wave function is regarded as a physical reality, which makes it possible to open up new possibilities in order to study the structure of the microcosm

DOI: 10.15587/1729-4061.2017.108831

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