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Apple Academic Press eBooks

Quantization of Energy Interactions

Г. А. Кораблев, G. E. Zaikov

Published Jul 22, 2013• 0 citations
Publisher

Abstract

Quantum concepts on atom and molecule composition constitute the foundation of modern natural science theories. Thus, in a stationary state the moment of electron motion amount equals the integral multiple from Plank’s constant. This main quantum number and three other together expressly characterize the state of any atom. The repetition factor of atom quantum characteristics is expressed in spectral data for both simple and complex structures.

DOI
10.1201/b15299-33

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Quantum concepts on atom and molecule composition constitute the foundation of modern natural science theories. Thus, in a stationary state the moment of electron motion amount equals the integral multiple from Plank’s constant. This main quantum number and three other together expressly characterize the state of any atom. The repetition factor of atom quantum characteristics is expressed in spectral data for both simple and complex structures.
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 topic is introduced through a consideration of the energy of photons and the transition between energy levels. This requires a knowledge of mathematical relationships and proportionality. The latter allows us to consider the forces between atoms, which can usefully be analysed in terms of stationary points, which is an important aspect of differential calculus. Complex numbers are revisited in the consideration of the quantum mechanics of a particle in a box, which introduces the concept of sequences and the use of standard integrals. The complex conjugate and the modulus of a complex number allow us to consider the quantum mechanics of the free particle. The hydrogen atom wavefunction requires knowledge of integration by parts, the calculus of the exponential function, multiple integration and the calculus of the trigonometric functions. Finally, we consider the use of determinants in the use of Hückel theory to study larger molecules.
Some preliminaries We have, until now, thought of atoms as tiny hard spheres that feel a force of attraction towards one another. We ignored the fact that an atom consists of a nucleus surrounded by one or more electrons. If we stopped at this, we would make little progress towards understanding the properties of solids, other than that the atoms may form crystals. We must therefore go on and take a look at the internal structure of the atom itself, and see how this changes when the atom is surrounded by other atoms in a crystal. We shall then find that we need a description that is somewhat removed from our everyday experience. There is a name for this description, quantum mechanics : mechanics, because it deals with the motion of objects, and quantum, because features of the motion, such as energy, are quantized , meaning that they can only have any one of a set of distinct values, and no other value in between. Imagine for example a car which is so constructed that it can travel only at speeds of 10, or 50, or 100 km per hour, and not at any other speed. Then we could say that the speed of the car is quantized. This idea of quantization is something alien to our usual way of thinking. After all, a car is able to go at any speed we like up to its maximum speed.
The modern physics is characterized by deeper and deeper penetration into the laws of the world of atoms and other minute particles of matter. These laws require not only new experimental techniques to be developed, but also new notions to formulate them. To describe atomic phenomena new methods that are completely different from those used to investigate larger objects of our world are required. The new problem of description of atomic objects is of particular practical importance since the arising notions could be applied to other fields of knowledge. Therefore on the ground of the modern physics some questions of the philosophical character arise. We are going to consider them here.
This paper aims to provide a thorough critical analysis of two foundational concepts in modern physics — the Landé g-factor and the electron spin quantum number 1/2. Through meticulous historical examination and logical analysis, this paper argues that these concepts are essentially mathematical fitting parameters introduced to bridge the gap between the old quantum theory and experimental data, lacking a solid foundation in physical mechanism. The core contradiction lies in the subsequent development of wave mechanics, which concluded that "the orbital angular momentum of the hydrogen atom ground state is zero," a conclusion that fundamentally conflicts with observational facts such as the Stern-Gerlach experiment, forcing the spin concept to assume a "remedial" role it never needed to bear. As a solution, this paper presents a new framework based on the "Great Tao Model" and the "Unified Theory of Atomic and Molecular Structure." This framework firmly returns to the realism of classical physics, affirms the orbital motion of electrons around the nucleus and their intrinsic angular momentum, and interprets spin as a real mechanical motion. Crucially, this theory naturally derives the universal magnetic moment-angular momentum relation μ = (e/m) L from the "Existence Field" principle, eliminating the need for any artificial correction factors. Based on this, the paper successfully provides a unified and self-consistent explanation for key phenomena such as the Stern-Gerlach experiment and the normal and anomalous Zeeman effects, thereby achieving a simpler and more fundamental description of physics at the atomic scale.