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

Authors

  • Nail Valishin Kazan National Research Technical University named after A. N. Tupolev-KAI K. Marksa str., 10, Kazan, Russia, 420111, Russian Federation
  • Sergey Moiseev Kazan Quantum Center KNITU-KAI Kazan National Research Technical University named after A. N. Tupolev-KAI K. Marksa str., 10, Kazan, Russia, 420111, Russian Federation

DOI:

https://doi.org/10.15587/1729-4061.2017.108831

Keywords:

variational principle, direct problem of dynamics, inverse problem of dynamics, optical-mechanical analogy, wave motion, trajectory motion, wave function, wave equation

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

Author Biographies

Nail Valishin, Kazan National Research Technical University named after A. N. Tupolev-KAI K. Marksa str., 10, Kazan, Russia, 420111

PhD, Associate Professor

Department of Special Mathematics

Sergey Moiseev, Kazan Quantum Center KNITU-KAI Kazan National Research Technical University named after A. N. Tupolev-KAI K. Marksa str., 10, Kazan, Russia, 420111

Doctor of Physical and Mathematical Sciences, Professor

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Published

2017-08-30

How to Cite

Valishin, N., & Moiseev, S. (2017). A method of V-function: ultimate solution to the direct and inverse problems of dynamics for a hydrogen-like atom. Eastern-European Journal of Enterprise Technologies, 4(5 (88), 23–32. https://doi.org/10.15587/1729-4061.2017.108831

Issue

Vol. 4 No. 5 (88) (2017): Applied physics

Section

Applied physics

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Copyright (c) 2017 Nail Valishin, Sergey Moiseev

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