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International Journal of Scientific and Innovative Mathematical Research

Establishing the Equation of the Wave Function and the System Model (p, m, v)

Published Jan 1, 2020• 1 citation
Publisher

Abstract

In this section a relation which establishes universal parameters of the matter will give us a new model that I call them the model (ρ, m, v) but in this model I will put relations between the parameters of the matter and the wave function and I'm going to explain that they are linking together the wave function plays the role of the wave function of matter and energy at the same time this gives us access to a new aspect that is a relationship of the wave function with mass and density makes it easier for us to exploit other relationships for the new model.

DOI
10.20431/2347-3142.0807003

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In this section, a relation which establishes universal parameters of the matter will give us a new model that I call them the model (ρ, m, and v) but, in this model, I will put relations between the parameters of the matter and the wave function and I’m going to explain that they are linking together the wave function plays the role of the wave function of matter and energy at the same time this gives us access to a new aspect that is a relationship of the wave function with mass and density makes it easier for us to exploit other relationships for the new model.
In this section, a relation which establishes universal parameters of the matter will give us a new model that I call them the model (ρ, m, and v) but, in this model, I will put relations between the parameters of the matter and the wave function and I’m going to explain that they are linking together the wave function plays the role of the wave function of matter and energy at the same time this gives us access to a new aspect that is a relationship of the wave function with mass and density makes it easier for us to exploit other relationships for the new model.
This article is a continuation of Part(I) to demonstrate more aspects for a successful merge of classical mechanics to the quantum theory. The article starts first with the deduction of the general form of the complimentary energy, next a robust firm mathematical proof is given indicates that the complimentary energy has a wave nature and it is a potential energy, then the radiation condition has been determined, a vector formula expresses the corresponding force was deduced and this force was called adhesion force. A mathematical convergence process has proved the duality of the electromagnetic wave parameters and particle parameters, which results in the existence of a “wave-particle” object. While finding the relationship between the electromagnetic wave parameters and particle parameters, a mathematical relationship was found indicating that not every moving charged mass generates a magnetic field. This relationship for the mass was linked to the effective mass tensor, The geometric representation of the constant energy surface and its relationship to the energy levels of both the orbital model (Bohr model) and the cloud model for different geometric 3D shapes were investigated as a sample of the possible geometric interpretations of the energy equation, that is by employing the triangle method, it is possible to create a geometric representation of the constant energy surfaces. The relation between the energy levels, quantum numbers, and band width is represented geometrically. As a result of proving the relationship between the motion of an electromagnetic wave and the motion of a particle associated with the wave, two new, unprecedented mathematical formulas were developed. The first formula specifies a moving charged mass and its relationship to the resulting wavelength. Thus, the radius of the charged mass is obtained in terms of its wavelength and mass density. The second formula specifies the kinetic energy of a photon. The grand potentials are the potential energy of the Newton’s Law of Universal Gravitation, Coulomb’s Law, and Inverse Square Law of Electromagnetic Waves Intensity. From the potential energy of Newton’s law of universal gravitation, the wavelength of the gravitational wave, as well as the wavelength of quantum gravity were deduced. A mathematical relationship was then deduced that determines the lengths of the functions of conic sections, and in particular the length of perimeter of ellipses. From the potential energy of Coulomb’s law of attraction, a mathematical formulation of the energy levels in general for any atom of an element was obtained. This mathematical formulation was compared with the results obtained by Bohr and Schrödinger for the hydrogen atom. As for the inverse square law of electromagnetic radiation intensity, several innovative mathematical equations have been deduced that link different parameters together. Following the contents of this article requires to be quite familiar with the contents of the first part with the same title, as well as a complete understanding of the concepts of intermediate parameters derived and used in the various equations. Otherwise, it will be extremely difficult to follow the contents of this article.