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.

Mar 22, 20210 citations

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

Mohamed Daris

Journal of Physical MathematicsJan 1, 20180 citations

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

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.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.

International Journal of Scientific and Innovative Mathematical ResearchJan 1, 20201 citation

Theoretical Background

Anne‐Marie Sapse

Inadequate descriptions of atoms and molecules by the methods of classical physics led researchers to propose new ways to describe physical reality, giving birth to a totally new science, quantum mechanics. The methods of quantum mechanics are based on the introduction of a wave function, whose physical meaning is related to the probability of finding a certain particle, at a certain time in a volume element, positioned between x and x + dx in the x = direction, between y and y + dy in the y = direction, and between z and z + dz in the z = direction at certain time t. This wave function Ψ satisfies the Schrödinger equation, $\left( { - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + v} \right)\Psi = {\rm E}\Psi,\hbar = \frac{h}{{2\pi }},$ or for short, HΨ = EΨ, where H, the Hamiltonian operator, is defined by the expression $H = - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + V;$ h is Planck’s constant; ∇2 is the sum of the partial second derivatives with respect to x, y, and z; m is the mass of the particle; and V is the potential energy of the system. The Hamiltonian H represents the quantum equivalent of the sum of the kinetic energy and potential energy, with V being the potential energy operator and $\frac{{ - {\hbar ^2}}}{{2m}}{\nabla ^2}$ the kinetic energy operator. Finally, E is the total energy of the system and is a number, not an operator.Inadequate descriptions of atoms and molecules by the methods of classical physics led researchers to propose new ways to describe physical reality, giving birth to a totally new science, quantum mechanics. The methods of quantum mechanics are based on the introduction of a wave function, whose physical meaning is related to the probability of finding a certain particle, at a certain time in a volume element, positioned between x and x + dx in the x = direction, between y and y + dy in the y = direction, and between z and z + dz in the z = direction at certain time t. This wave function Ψ satisfies the Schrödinger equation, $$ \left( { - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + v} \right)\Psi = {\rm E}\Psi,\hbar = \frac{h}{{2\pi }}, $$ or for short, HΨ = EΨ, where H, the Hamiltonian operator, is defined by the expression $$ H = - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + V; $$ h is Planck’s constant; ∇2 is the sum of the partial second derivatives with respect to x, y, and z; m is the mass of the particle; and V is the potential energy of the system. The Hamiltonian H represents the quantum equivalent of the sum of the kinetic energy and potential energy, with V being the potential energy operator and $$ \frac{{ - {\hbar ^2}}}{{2m}}{\nabla ^2} $$ the kinetic energy operator. Finally, E is the total energy of the system and is a number, not an operator.

Birkhäuser Boston eBooksJan 1, 20002 citations

A Link Merges Classical Mechanics to Quantum Theory (Part II)

Alaa S. Bayoumi

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.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.

Journal of Applied Mathematics and PhysicsJan 1, 20251 citation

Search for quantum gravity in space

R. Bingham, José Tito Mendonça, Charles H.-T. Wang

One of the biggest unsolved problems in fundamental physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance makes the issue particularly evasive. Recent models of decoherence demonstrated that conformal fluctuations of spacetime can change the correlation function of matter-waves. Latest progress on conformal decomposition in canonical gravity makes it possible for these decoherence models to be developed without freezing any degrees of freedom for general relativity. The new approach allows the roles of the conformal field and (spin-2) gravitational waves to be identified in the Brownian motion principle based on which Planck scale physics could be accessed. A spacecraft mission called Hyper was proposed to conduct matter-wave experiments in space. Orders of magnitude improvement may be gained by going into orbit reducing the effects of environmental interactions. Such experiments could put constraints on the upper bounds of measurements of decoherence of a matter-wave interferometer due to quantum fluctuations of spacetime.One of the biggest unsolved problems in fundamental physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance makes the issue particularly evasive. Recent models of decoherence demonstrated that conformal fluctuations of spacetime can change the correlation function of matter-waves. Latest progress on conformal decomposition in canonical gravity makes it possible for these decoherence models to be developed without freezing any degrees of freedom for general relativity. The new approach allows the roles of the conformal field and (spin-2) gravitational waves to be identified in the Brownian motion principle based on which Planck scale physics could be accessed. A spacecraft mission called Hyper was proposed to conduct matter-wave experiments in space. Orders of magnitude improvement may be gained by going into orbit reducing the effects of environmental interactions. Such experiments could put constraints on the upper bounds of measurements of decoherence of a matter-wave interferometer due to quantum fluctuations of spacetime.

Mar 29, 20060 citations

\left( { - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + v} \right)\Psi = {\rm E}\Psi,\hbar = \frac{h}{{2\pi }},

or for short, HΨ = EΨ, where H, the Hamiltonian operator, is defined by the expression

H = - \frac{{{\hbar ^2}}}{{2m}}{\nabla ^2} + V;

h is Planck’s constant; ∇2 is the sum of the partial second derivatives with respect to x, y, and z; m is the mass of the particle; and V is the potential energy of the system. The Hamiltonian H represents the quantum equivalent of the sum of the kinetic energy and potential energy, with V being the potential energy operator and

\frac{{ - {\hbar ^2}}}{{2m}}{\nabla ^2}

the kinetic energy operator. Finally, E is the total energy of the system and is a number, not an operator.