Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

European Chemical Bulletin

ON ENERGY PRINCIPLES OF STRUCTURAL INTERACTIONS

Г. А. Кораблев, Кодолов Владимир Иванович, Gennady Efremovich Zaikov, N. G. Petrova

Published Jun 15, 2016• 0 citations
Publisher

Abstract

The notion of spatial-energy parameter (P-parameter) is introduced based on the modified Lagrangian equation for relative motion of two interacting material points, which is a complex characteristic of important atomic values. Wave properties of P-parameter are found, its wave equation having a formal analogy with the equation of Ψ-function is given. In the systems in which the interactions proceed along the potential gradient (positive performance) the resulting potential energy is found based on the principle of adding reciprocals of the corresponding energies of subsystems. Some correlations of P-parameter values with Lagrangian and Hamiltonian functions are obtained.

DOI
10.17628/ecb.2016.5.293-299

Related papers

A Technical note on Quantum and Wave Characteristics of Spatial-Energy Interactions

It is demonstrated that for two-particle interactions the principle of adding reciprocals of energy characteristics of subsystems is performed for processes flowing by the potential gradient, and the principle of their algebraic addition for the processes against the potential gradient.

Apple Academic Press eBooks•Nov 21, 2014•0 citations

Quantum and Wave Characteristics of Spatial-Energy Interactions

Г. А. Кораблев, Gennady Efremovich Zaikov

It is demonstrated that for two-particle interactions the principle of adding reciprocals of energy characteristics of subsystems is performed for processes flowing by the potential gradient, and the principle of their algebraic addition – for the processes against the potential gradient.

Apple Academic Press eBooks•May 7, 2014•1 citation

OBTAINING MACROMECHANICAL VALUES USING QUANTUM-MECHANICAL DIFFERENTIAL EQUATIONS

I.P. POPOV

The wave function Ψ satisfies the Schrödinger equation for a free particle. Formally, the Schrödinger equation generates the magnitude of mechanical motion of the zero order 0 p = mv 0 (in the sense that it is contained in the Schrödinger equation. Comparison of the wave function Ψ and its gradient implies a formal analogue of the Schrödinger equation, which generates the magnitude of mechanical motion of the first order 1 p = mv 1. From the comparison of the wave function and its time derivative yields a formal analogue of the Schrödinger equation, which generates the magnitude of mechanical motion of the second order 2 p = mv 2/2!. The values of mechanical motion of the zero, first, and second orders are known.Obviously, other formal analogs of the Schrödinger equation can generate mechanical motion of other orders.The aim of the work is to establish such quantities and related regularities that may be of interest, which makes the study relevant. hovering. Then the spatial derivatives will be one-dimensional. The magnitude of the mechanical movement of the third order is 3 p = mv 3/3!. This value is Umov's integral vector for kinetic energy. The magnitude of the mechanical movement minus the first order -1 p = mv -1 is a reverse impulse. The meaning of this quantity and its relevance is established by the theorem: in a hy- drogen-like atom, the quantity m v-1 is quantized. A fixed (unchanged) quantum is a quantity m v-1 correspond- e e 0 ing to the basic energy level. Almost all of the results obtained were a consequence of the use of quantum mechanical differential equations, however, the results themselves are predominantly macromechanical. The quantities of mechanical motion of various orders are generated by formal analogs of the Schrödinger equation. In all formal analogs of the Schrödinger equation, the orders of the partial derivatives differ by one. For quantities of motion with a positive degree of velocity, the order of the temporal derivatives is higher than that of the spatial ones. For quantities with a negative degree, the order of spatial derivatives is higher.

Izvestia Ufimskogo Nauchnogo Tsentra RAN•Sep 16, 2022•0 citations

Квантовые и волновые характеристики пространственно-энергетических взаимодействий

Кораблев Григорий Андреевич, Заиков Геннадий Ефремович

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.

Вестник Волгоградского государственного университета. Серия 10: Инновационная деятельность•Jan 1, 2014•0 citations

Fields and Quantum Physics

Jacques Vanier, Cipriana Tomescu

The Lagrangian could be written in terms of kinetic and potential energy, functions of coordinates and velocity and the amplitude of the fields at that point. The essential condition is that the Lagrangian assumed for the field, when studied with Lagrange’s equation, gives Maxwell’s equations as solution and leads to the same wave equation. There are many other fields of physics and many mechanical systems to which the Lagrangian approach can be applied. The goal of the present text is to introduce the beginner to the least action principle and the Lagrangian approach in an elementary way. The chapter argues that the Lagrangian chosen for the fields involved must be an expression that leads to those fields and equations. In wave mechanics, particle properties are described by a so-called wave representing the classical matter field ψ used in Schrodinger’s approach of wave mechanics.

CRC Press eBooks•Jan 15, 2019•0 citations

Analysis and Application of Lagrangian Function and Hamilton′s Principle in the Quantum Wave Field

Changrong Wang

By analysing the applied conditions of lagrangian function and Hamilton's principle in the quantum wave field,we have deduced the formality of its field equation.In addition,we have made in detail its calculation of the kinetic energy of the particle with a potential energy V(x) in the wave field.

Journal of Hubei Institute for Nationalities•Jan 1, 2002•0 citations
The notion of spatial-energy parameter (P-parameter) is introduced based on the modified Lagrangian equation for relative motion of two interacting material points, which is a complex characteristic of important atomic values. Wave properties of P-parameter are found, its wave equation having a formal analogy with the equation of Ψ-function is given. In the systems in which the interactions proceed along the potential gradient (positive performance) the resulting potential energy is found based on the principle of adding reciprocals of the corresponding energies of subsystems. Some correlations of P-parameter values with Lagrangian and Hamiltonian functions are obtained.
The wave function Ψ satisfies the Schrödinger equation for a free particle. Formally, the Schrödinger equation generates the magnitude of mechanical motion of the zero order 0 p = mv 0 (in the sense that it is contained in the Schrödinger equation. Comparison of the wave function Ψ and its gradient implies a formal analogue of the Schrödinger equation, which generates the magnitude of mechanical motion of the first order 1 p = mv 1. From the comparison of the wave function and its time derivative yields a formal analogue of the Schrödinger equation, which generates the magnitude of mechanical motion of the second order 2 p = mv 2/2!. The values of mechanical motion of the zero, first, and second orders are known.Obviously, other formal analogs of the Schrödinger equation can generate mechanical motion of other orders.The aim of the work is to establish such quantities and related regularities that may be of interest, which makes the study relevant. hovering. Then the spatial derivatives will be one-dimensional. The magnitude of the mechanical movement of the third order is 3 p = mv 3/3!. This value is Umov's integral vector for kinetic energy. The magnitude of the mechanical movement minus the first order -1 p = mv -1 is a reverse impulse. The meaning of this quantity and its relevance is established by the theorem: in a hy- drogen-like atom, the quantity m v-1 is quantized. A fixed (unchanged) quantum is a quantity m v-1 correspond- e e 0 ing to the basic energy level. Almost all of the results obtained were a consequence of the use of quantum mechanical differential equations, however, the results themselves are predominantly macromechanical. The quantities of mechanical motion of various orders are generated by formal analogs of the Schrödinger equation. In all formal analogs of the Schrödinger equation, the orders of the partial derivatives differ by one. For quantities of motion with a positive degree of velocity, the order of the temporal derivatives is higher than that of the spatial ones. For quantities with a negative degree, the order of spatial derivatives is higher.
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.
The Lagrangian could be written in terms of kinetic and potential energy, functions of coordinates and velocity and the amplitude of the fields at that point. The essential condition is that the Lagrangian assumed for the field, when studied with Lagrange’s equation, gives Maxwell’s equations as solution and leads to the same wave equation. There are many other fields of physics and many mechanical systems to which the Lagrangian approach can be applied. The goal of the present text is to introduce the beginner to the least action principle and the Lagrangian approach in an elementary way. The chapter argues that the Lagrangian chosen for the fields involved must be an expression that leads to those fields and equations. In wave mechanics, particle properties are described by a so-called wave representing the classical matter field ψ used in Schrodinger’s approach of wave mechanics.