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Journal of Physics Conference Series

On the controllability of a quantum object

N T Valishin

Published Dec 1, 2019• 0 citations
Publisher

Abstract

Abstract On the basis of the V-function method, the physical statement of controllability as a wave motion of an object to a new state is carried out. It follows from the V-function method that the wave motion of an object is inextricably linked with its trajectory. It is shown that controllability as an object leaves the state occurs in the direction of the gradient of the wave function.

DOI
10.1088/1742-6596/1399/2/022010

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Abstract On the basis of the V-function method, the physical statement of controllability as a wave motion of an object to a new state is carried out. It follows from the V-function method that the wave motion of an object is inextricably linked with its trajectory. It is shown that controllability as an object leaves the state occurs in the direction of the gradient of the wave function.
Abstract Based on the V -function method, the properties of wave nature of object motion are studied for object uniform motion with constant speed and for harmonic oscillator. It follows from the V -function method that object wave motion is inseparably linked with its trajectory motion. The V -function method consists of the principle of local variation and a new statement of the direct and inverse dynamics problems. The proposed approach made it possible to make the optico-mechanical analogy that obtained a new continuation. A comparison is made with the results obtained by Schrödinger for a harmonic oscillator.
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.
Abstract On the basis of the V-function method, an optical-mechanical analogy is carried out; and further it receives a new continuation. In particular, the equality of the phase velocity of the wave and the velocity of the particle is shown. It is noted that according to its physical meaning the wave characterizes the properties of the action that manifests itself in the motion of the particle. The V-function method is based on the concept of a process-state and it consists of a local variational principle, a new formulation of the direct and inverse problem of dynamics. According to the V-function method, the trajectory motion of an object is associated with its wave motion. In this case it is assumed that there is an explicit connection between the trajectory and wave equations of the object. The application of the V-function method for the case of rectilinear motion of an object is shown.
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
Aiming at providing an objective motion picture for the microscopic object described by the wave function, new analysis about motion is presented by use of the point set theory in mathematics, through which we show that a new kind of motion named quantum discontinuous motion is the general motion mode of the particle, while classical continuous motion is just one kind of extremely peculiar motion, and the wave function in quantum mechanics proves to be the very mathematical complex describing the particle undergoing the quantum discontinuous motion. Furthermore, Schroedinger equation of the wave function is shown to be the simplest nonrelativistic evolution equation for the particle undergoing the new motion, and the consistent axiom system of quantum mechanics is also deduced out. At last, we demonstrate that present quantum measurement theories just confirm the existence of the new motion of the microscopic particle described by the wave function, and the weird displays of the wave function in microscopic world are also physically explained in terms of the new motion.
It is shown that the wave function describes the state of the statistical ensemble E[S] of individual particles, or the statistical average particle . This result follows from the fact that in the classical limit h=0 the Schroedinger equation turns to the dynamic equations for the statistical ensemble of classical particles. The statement that the wave function describes the state of an individual particle is incompatible with the quantum mechanics formalism. It is shown that the statistical interpretation of quantum mechanics is a corollary of the fact, that the QM formalism is the technique of the statistical ensemble description, restricted by constraints of the dynamic equation linearity.