In a previous, primary treatise of the author the mathematical description of electron trajectories in the excited states of the H-atom could be demonstrated, starting from Bohr’s original model but modifying it thre...In a previous, primary treatise of the author the mathematical description of electron trajectories in the excited states of the H-atom could be demonstrated, starting from Bohr’s original model but modifying it three dimensionally. In a subsequent treatise, Bohr’s theorem of an unalterable angular momentum h/2π, determining the ground state of the H-atom, was revealed as an inducement by the—unalterable—electron spin. Starting from this presumption, a model of the H2-molecule could be created which exhibits well-defined electron trajectories, and which enabled computing the bond length precisely. In the present treatise, Bohr’s theorem is adapted to the atom models of helium and of neon. But while this was feasible exactly in the case of helium, the neon atom turned out to be too complex for a mathematical modelling. Nevertheless, a rough ball-and-stick model can be presented, assuming electron rings instead of electron clouds, which in the outer shell are orientated as a tetrahedron. It entails the principal statement that the neon atom does not represent a static construction with constant electron distances and velocities, but a pulsating dynamic one with permanently changing internal distances. Thus, the helium atom marks the limit for precisely describing an atom, whereby at and under this limit such a precise description is feasible, being also demonstrated in the author’s previous work. This contradicts the conventional quantum mechanical theory which claims that such a—locally and temporally—precise description of any atom or molecule structure is generally not possible, also not for the H2-molecule, and not even for the H-atom.展开更多
Proceeding from the double-cone model of Helium, based on Bohr’s theorem and recently published in?[13], a spherical modification could be made by introducing a second electron rotation which exhibits a rotation axis...Proceeding from the double-cone model of Helium, based on Bohr’s theorem and recently published in?[13], a spherical modification could be made by introducing a second electron rotation which exhibits a rotation axis perpendicular to the first one. Thereby, each rotation is induced by the spin of one electron. Thus the trajectory of each electron represents the superposition of two separate orbits, while each electron is always positioned opposite to the other one. Both electron velocities are equal and constant, due to their mutual coupling. The 3D electron orbits could be 2D-graphed by separately projecting them on the x/z-plane of a Cartesian coordinate system, and by plotting the evaluated x-, y- and z-values versus the rotation angle. Due to the decreased electron velocity, the resulting radius is twice the size of the one in the double-cone model. Even if distinct evidence is not feasible, e.g. by means of X-ray crystallographic data, this modified model appears to be the more plausible one, due to its higher cloud coverage, and since it comes closer to Kimball’s charge cloud model.展开更多
The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special r...The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.展开更多
In this work, we reanalyzed the movement of an electron in the electrostatic field of nucleus. The trajectory of the electron’s motion is an ellipse with a minor semiaxis, tending towards zero. From a mathematical po...In this work, we reanalyzed the movement of an electron in the electrostatic field of nucleus. The trajectory of the electron’s motion is an ellipse with a minor semiaxis, tending towards zero. From a mathematical point of view the movement of an electron in such an orbit will be equivalent to the oscillation of an electron. The action produced by electrons in movement between stationary points is discrete and proportional to a Planck constant. This condition sets the allowable values of the electron energy and the radius of their orbit. Electrons on the same shell perform symmetric synchronous oscillations. Their frequency is of the order of 1016 Hz. Most of the time the electrons are located on the periphery of the atom, periodically they simultaneously rush to the nucleus, the atom rapidly compresses and immediately decompresses, i.e. pulsates. The model gives Bohr formula for the energy of single-electron atom and suitable values of ionization potentials of the atoms of the second period of the Periodic Table.展开更多
We evaluate three of the quantum constants of hydrogen, the electron, e<sup>-</sup>, the Bohr radius, a<sub>0</sub>, and the Rydberg constants, , as natural unit frequency equivalents, v. This ...We evaluate three of the quantum constants of hydrogen, the electron, e<sup>-</sup>, the Bohr radius, a<sub>0</sub>, and the Rydberg constants, , as natural unit frequency equivalents, v. This is equivalent to Planck’s constant, h, the speed of light, c, and the electron charge, e, all scaled to 1 similar in concept to the Hartree atomic, and Planck units. These frequency ratios are analyzed as fundamental coupling constants. We recognize that the ratio of the product of 8π<sup>2</sup>, the v<sub>e</sub><sub>-</sub> times the v<sub>R</sub> divided by v<sub>a</sub><sub>0</sub> squared equals 1. This is a power law defining Planck’s constant in a dimensionless domain as 1. We also find that all of the possible dimensionless and dimensioned ratios correspond to other constants or classic relationships, and are systematically inter-related by multiple power laws to the fine structure constant, α;and the geometric factors 2, and π. One is related to an angular momentum scaled by Planck’s constant, and another is the kinetic energy law. There are harmonic sinusoidal relationships based on 2π circle geometry. In the dimensionless domain, α is equivalent to the free space constant of permeability, and its reciprocal to permittivity. If any two quanta are known, all of the others can be derived within power laws. This demonstrates that 8π2 represents the logical geometric conversion factor that links the Euclid geometric factors/three dimensional space, and the quantum domain. We conclude that the relative scale and organization of many of the fundamental constants even beyond hydrogen are related to a unified power law system defined by only three physical quanta of v<sub>e</sub><sub>-</sub>, v<sub>R</sub>, and v<sub>a</sub><sub>0</sub>.展开更多
The present article is a continuation of a recently published paper [1] in which we have modeled the composition and structure of neutrons and other hadrons using the Rotating Lepton Model (RLM) which is a Bohr type m...The present article is a continuation of a recently published paper [1] in which we have modeled the composition and structure of neutrons and other hadrons using the Rotating Lepton Model (RLM) which is a Bohr type model employing the relativistic gravitational attraction between three ultrafast rotating neutrinos as the centripetal force. The RLM accounts for special relativity and also for the De Broglie equation of quantum mechanics. In this way this force was shown to reach the value of the Strong Force while the values of the masses of the rotating relativistic neutrinos reach those of quarks. Masses computed for twelve hadrons and bosons are in very close (~2%) agreement with the experimental values. Here we use the same RLM approach to describe the composition and structure and to compute the masses of Pions and Kaons which are important zero spin mesons. Contrary to hadrons and bosons which have been found via the RLM to comprise the heaviest neutrino eigenmass m<sub>3</sub>, in the case of mesons the intermediate neutrino mass eigenstate m<sub>2</sub> is found to play the dominant role. This can explain why the lowest masses of mesons are generally smaller than those of hadrons and bosons. Thus in the case of Pions it is found that they comprise three rotating m<sub>2</sub> mass eigenstate neutrinos and the computed mass of 136.6 MeV/c<sup>2</sup> is in good agreement with the experimental value of 134.977 MeV/c<sup>2</sup>. The Kaon structure is found to consist of six m<sub>2</sub> mass eigenstate neutrinos arranged in two parallel pion-type rotating triads. The computed Kaon mass differs less that 2% from the experimental K<sup>±</sup> and K°values of 493.677 MeV/c<sup>2</sup> and 497.648 MeV/c<sup>2</sup> respectively. This, in conjunction with the experimentally observed decay products of the Kaons, provides strong support for the proposed K structure.展开更多
In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental po...In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.展开更多
The generation of an attosecond pulse in the ultraviolet range is described in the terms of the catastrophe theory. A simple criterion of tunneling is proposed. The criterion allows constructing the quasiclassical mod...The generation of an attosecond pulse in the ultraviolet range is described in the terms of the catastrophe theory. A simple criterion of tunneling is proposed. The criterion allows constructing the quasiclassical model of the generator of attosecond laser pulses based on the interaction of an electric field of extremely powerful femtosecond pulse with the valence electron in the potential well of the gas atom.展开更多
文摘In a previous, primary treatise of the author the mathematical description of electron trajectories in the excited states of the H-atom could be demonstrated, starting from Bohr’s original model but modifying it three dimensionally. In a subsequent treatise, Bohr’s theorem of an unalterable angular momentum h/2π, determining the ground state of the H-atom, was revealed as an inducement by the—unalterable—electron spin. Starting from this presumption, a model of the H2-molecule could be created which exhibits well-defined electron trajectories, and which enabled computing the bond length precisely. In the present treatise, Bohr’s theorem is adapted to the atom models of helium and of neon. But while this was feasible exactly in the case of helium, the neon atom turned out to be too complex for a mathematical modelling. Nevertheless, a rough ball-and-stick model can be presented, assuming electron rings instead of electron clouds, which in the outer shell are orientated as a tetrahedron. It entails the principal statement that the neon atom does not represent a static construction with constant electron distances and velocities, but a pulsating dynamic one with permanently changing internal distances. Thus, the helium atom marks the limit for precisely describing an atom, whereby at and under this limit such a precise description is feasible, being also demonstrated in the author’s previous work. This contradicts the conventional quantum mechanical theory which claims that such a—locally and temporally—precise description of any atom or molecule structure is generally not possible, also not for the H2-molecule, and not even for the H-atom.
文摘Proceeding from the double-cone model of Helium, based on Bohr’s theorem and recently published in?[13], a spherical modification could be made by introducing a second electron rotation which exhibits a rotation axis perpendicular to the first one. Thereby, each rotation is induced by the spin of one electron. Thus the trajectory of each electron represents the superposition of two separate orbits, while each electron is always positioned opposite to the other one. Both electron velocities are equal and constant, due to their mutual coupling. The 3D electron orbits could be 2D-graphed by separately projecting them on the x/z-plane of a Cartesian coordinate system, and by plotting the evaluated x-, y- and z-values versus the rotation angle. Due to the decreased electron velocity, the resulting radius is twice the size of the one in the double-cone model. Even if distinct evidence is not feasible, e.g. by means of X-ray crystallographic data, this modified model appears to be the more plausible one, due to its higher cloud coverage, and since it comes closer to Kimball’s charge cloud model.
文摘The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.
文摘In this work, we reanalyzed the movement of an electron in the electrostatic field of nucleus. The trajectory of the electron’s motion is an ellipse with a minor semiaxis, tending towards zero. From a mathematical point of view the movement of an electron in such an orbit will be equivalent to the oscillation of an electron. The action produced by electrons in movement between stationary points is discrete and proportional to a Planck constant. This condition sets the allowable values of the electron energy and the radius of their orbit. Electrons on the same shell perform symmetric synchronous oscillations. Their frequency is of the order of 1016 Hz. Most of the time the electrons are located on the periphery of the atom, periodically they simultaneously rush to the nucleus, the atom rapidly compresses and immediately decompresses, i.e. pulsates. The model gives Bohr formula for the energy of single-electron atom and suitable values of ionization potentials of the atoms of the second period of the Periodic Table.
文摘We evaluate three of the quantum constants of hydrogen, the electron, e<sup>-</sup>, the Bohr radius, a<sub>0</sub>, and the Rydberg constants, , as natural unit frequency equivalents, v. This is equivalent to Planck’s constant, h, the speed of light, c, and the electron charge, e, all scaled to 1 similar in concept to the Hartree atomic, and Planck units. These frequency ratios are analyzed as fundamental coupling constants. We recognize that the ratio of the product of 8π<sup>2</sup>, the v<sub>e</sub><sub>-</sub> times the v<sub>R</sub> divided by v<sub>a</sub><sub>0</sub> squared equals 1. This is a power law defining Planck’s constant in a dimensionless domain as 1. We also find that all of the possible dimensionless and dimensioned ratios correspond to other constants or classic relationships, and are systematically inter-related by multiple power laws to the fine structure constant, α;and the geometric factors 2, and π. One is related to an angular momentum scaled by Planck’s constant, and another is the kinetic energy law. There are harmonic sinusoidal relationships based on 2π circle geometry. In the dimensionless domain, α is equivalent to the free space constant of permeability, and its reciprocal to permittivity. If any two quanta are known, all of the others can be derived within power laws. This demonstrates that 8π2 represents the logical geometric conversion factor that links the Euclid geometric factors/three dimensional space, and the quantum domain. We conclude that the relative scale and organization of many of the fundamental constants even beyond hydrogen are related to a unified power law system defined by only three physical quanta of v<sub>e</sub><sub>-</sub>, v<sub>R</sub>, and v<sub>a</sub><sub>0</sub>.
文摘The present article is a continuation of a recently published paper [1] in which we have modeled the composition and structure of neutrons and other hadrons using the Rotating Lepton Model (RLM) which is a Bohr type model employing the relativistic gravitational attraction between three ultrafast rotating neutrinos as the centripetal force. The RLM accounts for special relativity and also for the De Broglie equation of quantum mechanics. In this way this force was shown to reach the value of the Strong Force while the values of the masses of the rotating relativistic neutrinos reach those of quarks. Masses computed for twelve hadrons and bosons are in very close (~2%) agreement with the experimental values. Here we use the same RLM approach to describe the composition and structure and to compute the masses of Pions and Kaons which are important zero spin mesons. Contrary to hadrons and bosons which have been found via the RLM to comprise the heaviest neutrino eigenmass m<sub>3</sub>, in the case of mesons the intermediate neutrino mass eigenstate m<sub>2</sub> is found to play the dominant role. This can explain why the lowest masses of mesons are generally smaller than those of hadrons and bosons. Thus in the case of Pions it is found that they comprise three rotating m<sub>2</sub> mass eigenstate neutrinos and the computed mass of 136.6 MeV/c<sup>2</sup> is in good agreement with the experimental value of 134.977 MeV/c<sup>2</sup>. The Kaon structure is found to consist of six m<sub>2</sub> mass eigenstate neutrinos arranged in two parallel pion-type rotating triads. The computed Kaon mass differs less that 2% from the experimental K<sup>±</sup> and K°values of 493.677 MeV/c<sup>2</sup> and 497.648 MeV/c<sup>2</sup> respectively. This, in conjunction with the experimentally observed decay products of the Kaons, provides strong support for the proposed K structure.
文摘In this work, we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case, the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K?× S1?defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube. Therefore, in three-dimensions, the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K?× S1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.
文摘The generation of an attosecond pulse in the ultraviolet range is described in the terms of the catastrophe theory. A simple criterion of tunneling is proposed. The criterion allows constructing the quasiclassical model of the generator of attosecond laser pulses based on the interaction of an electric field of extremely powerful femtosecond pulse with the valence electron in the potential well of the gas atom.
