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European Chemical Bulletin

CORPUSCULAR-WAVE PROCESSES IN QUANTUM TRANSITIONS

Г. А. Кораблев, N. G. Petrova

Published Aug 9, 2016• 0 citations
Publisher

Abstract

Two principles of adding energy characteristics of structural interactions are fulfilled if the process flows either along the potential gradient or against it. Transforming these rules onto the corpuscular-wave dualism, we can assume that corpuscular interactions flow along the potential gradient (principle of adding reciprocals of energies), and wave processes – against the potential gradient (principle of algebraic addition of energies). Such approach is confirmed by the empiric equation, in which the act of quantum action is narrowed to the energy redistribution in the system “particle-wave”. It is demonstrated that the angular vector of rotational-translation motion of electrons at quantum transitions changes in compliance with the quantum number of the square tangent of this angle.

DOI
10.17628/ecb.2016.5.339-344

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Two principles of adding energy characteristics of structural interactions are fulfilled if the process flows either along the potential gradient or against it. Transforming these rules onto the corpuscular-wave dualism, we can assume that corpuscular interactions flow along the potential gradient (principle of adding reciprocals of energies), and wave processes – against the potential gradient (principle of algebraic addition of energies). Such approach is confirmed by the empiric equation, in which the act of quantum action is narrowed to the energy redistribution in the system “particle-wave”. It is demonstrated that the angular vector of rotational-translation motion of electrons at quantum transitions changes in compliance with the quantum number of the square tangent of this angle.
Two principles of adding energy characteristics of structural interactions are fulfilled if the process flows either along the potential gradient or against it. Transforming these rules onto the corpuscular-wave dualism, we can assume that corpuscular interactions flow along the potential gradient (principle of adding reciprocals of energies), and wave processes—against the potential gradient (principle of algebraic addition of energies). Such approach is confirmed by the empiric equation, in which the act of quantum action is narrowed to the energy redistribution in the system “particle-wave.” It is demonstrated that the angular vector of rotational–translation motion of electrons at quantum transitions changes in compliance with the quantum number of the square tangent of this angle.
The quantum ideas about the structure of atoms and molecules are the foundation of modern scientific theories. So, the steady angular momentum of the electron is an integer multiple of Planck's constant. It is the principal quantum number, and three others in general uniquely characterize the state of any atom. The multiplicity of atomic quantum characteristics is manifested in the spectral data for simple and complex structures. The article shows that in two-particle interactions the principle of summing the inverse quantities of subsystems energetic characteristics is carried out during the processes which occur by potential gradient, and the principle of their algebraic addition during the processes which occur against potential gradient. The authors calculated the equation of dependence of spatial and energetic parameter of free atoms from their wave, spectral and frequency characteristics.
In this work we propose a new approach to the explanation of the nature of electron based on the corpuscular-wave monism using the further development of the optical-mechanical analogy to describe the physical reality. In this theory the motion of an electron is considered to occur along a trajectory the presence of which is a reflection of the existence of a particle, as well as it is assumed that any motion is defined by a wave V(x,t). It is assumed that there is an explicit relationship between the trajectory and wave equations of the electron, which are established on the basis of the local variational principle. In this approach, an electron wave propagating in free space takes along the electron trajectory. We used this theory to describe the electron motion in a hydrogen-like atom and found its stationary states. The energies of these states coincide with the known quantum mechanics solutions for the stationary energies of the hydrogen-like atom, however, in our approach the spatial trajectories of the electron have the form of the surfaces, which are formed in the region of nodes of the standing electron wave. These surfaces have the form of spheres for the spherical symmetrical electron states and the radii of these spheres coincide with the radii of the Bohr orbits of these states. Thus, in this approach the trajectory and wave measurements of the electron get a consistent spatial description that is inherent to the picture of the corpuscular-wave monism. We discuss the considerable correspondence of the proposed theory with the quantum mechanics results describing the stationary and non-stationary motions of the electron in the atom and their difference. We believe that measuring of the spatial configuration of the observed electron trajectory surfaces in an atom could be a deep examination of the standard quantum theory.
Since the interest in the quantum phenomena started, there have been two main approaches to the quantum theory, the first approach investigates the motion of a wave-particle object by assuming the wave has the characteristics of a moving particle, momentum and energy, this approach was developed by physicists Max Planck, Albert Einstein, and others. The second approach investigates the motion of a particle-wave object by assuming the particle has the characteristics of a moving wave, wavelength, wave vector, and frequency, this approach was developed by physicists De Broglie, Schrodinger and others which led to the presence of quantum mechanics. This article focuses on the second approach and merging it with classical mechanics. An early mathematical formulation for the quantum theory was proposed by De Broglie’s relations and later on, another formulation was given by Schrodinger’s equation. A successful attempt to bridge the gap between classical mechanics with quantum theory implemented via a mathematical derivation for De Broglie’s relations and Schrodinger formulation, The derivation process overcame a main obstacle was the convergence of the deterministic nature of classical mechanics with the probabilistic nature of the quantum theory by adopting an innovative method based upon replacing constant values in a deterministic relation with probabilistic variables in the same relation, and this led to switch the relation from deterministic representation to probabilistic representation. Both classical and quantum explanation are given for the deduced formulas. An energy approach is instrumented. Since classical mechanics formulas are not sufficient to explain the quantum phenomena, a new concept of complementary energy introduced in order to connect the parameters of a moving particle with the parameters of an associated wave, the value of the complementary energy for each particle adjusted the total energy equation of N moving particles without changing the magnitude of the total energy of a system of N particles. In special cases, the value of the complementary energy for some particles equals the value of the total energy for the particles. The derivation process indicates that complementary energy corresponds to the potential energy on the surface of the material which prevents the particles to escape from the boundary of the matter to the outer space and maintains its coherence, complementary energy concept also manifest the impact of the moving particles on a single particle due to the energy conveyed during direct contact in case of collision or by the remote influence through an existing field in the space, so it represents an energy of dual nature for both matter and radiation wave combined. The complementary energy is not introduced as mathematical assumption in order to manipulate the total energy equation, it’s actually exists in the total energy equation and its validity has not been applied before. A general format for any potential energy is obtained regardless the nature of field it represents (a universal format for potential energy) that is by using mathematical manipulation for the equation of total energy of N moving particles. The derivation process led to a particle-wave formula. The substitution into the particle-wave formula with the speed of light, De Broglie’s relations, revealed. Some additional applications for the particle-wave formula are suggested, also as a well known energy quantization formula obtained by applying all of De Broglie’s relation, a general energy, and speed formulas resulting during the derivation process. Matching time independent equation called Schrodinger’s amplitude equation with classical mechanics formulation demonstrated by deducing both the wave function and the magnitude of the wave vector from the classical formulation after converting it to probabilistic formulation. A dedicated section for wave function solutions for Schrodinger’s time dependent equation was given in terms of the wave functions and the magnitude of the wave vectors obtained from the matching process of Schrodinger’s amplitude equation with classical mechanics.