The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an...The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.展开更多
Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits...Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.展开更多
The discovery of a data based informational wave pattern infuses coherent entanglement into the system. This discovery of how to add coherent entanglement into the model provides the missing key, that has opened the d...The discovery of a data based informational wave pattern infuses coherent entanglement into the system. This discovery of how to add coherent entanglement into the model provides the missing key, that has opened the door to understanding the universe. It is found that the inclusion of coherence and entanglement at the start of the system is extremely simple and in fact it is so simple that it has simply been overlooked. Entanglement and coherence are the most fundamental aspects of our universe. It is demonstrated that the basic model of the hydrogen atom is made from the CMB. If we add entanglement into this basic model of the hydrogen atom a math system called Wave Pattern Entangled Math is unveiled. This system of wave interference mathematics creates a data system in which entanglement and coherence can easily be understood. The final outcome is an unbreakable pattern of information, including entangled energy, entropy, spin, universal expansion, compression, velocity of light, C2, and Quantum Coherence.展开更多
We develop the discrete derivatives representation method (DDR) to find the physical structures of the Schr?dinger equation in which the interpolation polynomial of Bernstein has been used. In this paper the particle ...We develop the discrete derivatives representation method (DDR) to find the physical structures of the Schr?dinger equation in which the interpolation polynomial of Bernstein has been used. In this paper the particle swarm optimization (PSO for short) has been suggested as a means to improve qualitatively the solu-tions. This approach is carefully handled and tested with a numerical example.展开更多
It is accepted that quantum mechanics (QM) describes motion of waves and particles. Therefore, we must use wave-particle duality (WPD), which is usually considered as one of the foundations of QM;however, WPD is well ...It is accepted that quantum mechanics (QM) describes motion of waves and particles. Therefore, we must use wave-particle duality (WPD), which is usually considered as one of the foundations of QM;however, WPD is well known as a self-contradictory concept. These contradictions insensibly spoil our subconscious thinking about the micro-world (MW). This article shows that known trials to solve these contradictions are erroneous. Quantum jumps (QJs) are shown to be very lame arguments for the real existence of particles. I offer rejecting the concept of particles and using their names as labels for types of corresponding waves. Thus, we can discard contradictions created by WPD. This approach is validated in the article by careful analysis of real calculation methods of quantum electrodynamics (QED). For the first time, it is noticed that proper 4-coordinates of particles are not in use in real calculations in QED. This implies that particles do not take part in real calculations, which describe properties of atoms and molecules. It follows that particles do not exist as such. Therefore, we must acknowledge that we actually use the names of “particles” merely as names of types of given waves, but not as real, physical objects.展开更多
Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relat...Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.展开更多
文摘The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.
文摘Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits with several walls in terms of Lagrangian instead of Hamiltonian resulted in a magnificent work. It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them a heuristic tool that lacks a sound mathematical definition. This paper aims to refute this prejudice, by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics. About a hundred years after the beginning of modern physics, it was realized that light could in fact show behavioral characteristics of both waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same dual behavior, which was later extended to atoms and molecules. We shall follow the method of integration with some modifications to construct a generalized Lebesgue-Bochner-Stieltjes (LBS) integral of the form , where u is a bilinear operator acting in the product of Banach spaces, f is a Bochner summable function, and μ is a vector-valued measure. We will demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with LBS integration approach.
文摘The discovery of a data based informational wave pattern infuses coherent entanglement into the system. This discovery of how to add coherent entanglement into the model provides the missing key, that has opened the door to understanding the universe. It is found that the inclusion of coherence and entanglement at the start of the system is extremely simple and in fact it is so simple that it has simply been overlooked. Entanglement and coherence are the most fundamental aspects of our universe. It is demonstrated that the basic model of the hydrogen atom is made from the CMB. If we add entanglement into this basic model of the hydrogen atom a math system called Wave Pattern Entangled Math is unveiled. This system of wave interference mathematics creates a data system in which entanglement and coherence can easily be understood. The final outcome is an unbreakable pattern of information, including entangled energy, entropy, spin, universal expansion, compression, velocity of light, C2, and Quantum Coherence.
文摘We develop the discrete derivatives representation method (DDR) to find the physical structures of the Schr?dinger equation in which the interpolation polynomial of Bernstein has been used. In this paper the particle swarm optimization (PSO for short) has been suggested as a means to improve qualitatively the solu-tions. This approach is carefully handled and tested with a numerical example.
文摘It is accepted that quantum mechanics (QM) describes motion of waves and particles. Therefore, we must use wave-particle duality (WPD), which is usually considered as one of the foundations of QM;however, WPD is well known as a self-contradictory concept. These contradictions insensibly spoil our subconscious thinking about the micro-world (MW). This article shows that known trials to solve these contradictions are erroneous. Quantum jumps (QJs) are shown to be very lame arguments for the real existence of particles. I offer rejecting the concept of particles and using their names as labels for types of corresponding waves. Thus, we can discard contradictions created by WPD. This approach is validated in the article by careful analysis of real calculation methods of quantum electrodynamics (QED). For the first time, it is noticed that proper 4-coordinates of particles are not in use in real calculations in QED. This implies that particles do not take part in real calculations, which describe properties of atoms and molecules. It follows that particles do not exist as such. Therefore, we must acknowledge that we actually use the names of “particles” merely as names of types of given waves, but not as real, physical objects.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10075080, 19847002, 19835010 and Major State Basic Research Development Program under Grant No. G20000774
文摘Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.
