A Method of V-Function and the Problems of Trajectory-Wave Dynamics

A. N. Tupolev

Published Jan 1, 2013• 0 citations

Abstract

The paper introduces a method of V-function, from which it follows that the trajectory motion of an object is connected with the wave motion. We formulate a local variational principle (LVP) and the basic theorems of the method of V-function, which allow a new statement of the direct and inverse dynamics problems. Based on the method of V-function, we consider the optical-mechanic analogy, which is presented in a new extended version and investigate the properties of the wave nature of electron motion in a hydrogen-like atom and the motion of an object (particle) for a harmonic oscillator. We demonstrate that in a physical sense, the wave V(x,t) characterizes the properties of an action showing itself in the motion of an object (particle). By its node, the wave is connected with the position of the particle and so leads it. The particle (trajectory) in its turn generates a wave propagating along it. We establish that the energy levels of a hydrogen-like atom, obtained using the method of V-function, correspond entirely to the classical results of quantum physics, while the energy levels of a harmonic oscillator do not contradict the known Schrodinger's results.

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