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 Schrodinger 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
Highlights
Variational principles and optical-mechanical analogy were essential for the development of quantum mechanics
L. de Broglie shed a new light on the optical-mechanical analogy [2,3,4]
He considered the correspondence between a wave and a particle based on equations (1) and (2), and on the basis of variational principles by Maupertuis and Fermat
Summary
На базе метода V-функции осуществляется продолжение оптико-механической аналогии. Указывается на наличие квантования энергии частицы, решения без частицы в случае прямолинейного равномерного движения с постоянной скоростью. Исследуются свойства волновой природы движения электрона в водородоподобном атоме как решение прямой задачи. Показывается способ нахождения конечного решения стационарного волнового уравнения. Ключевые слова: вариационный принцип, прямая задача динамики, обратная задача динамики, оптико-механическая аналогия, волновое движение, траекторное движение, волновая функция, волновое уравнение
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
