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 present approach is an advancement of the author’s former attempts to develop an atom model of Helium with well-defined electron trajectories. Thus it calls in question the traditional quantum mechanics which ass...The present approach is an advancement of the author’s former attempts to develop an atom model of Helium with well-defined electron trajectories. Thus it calls in question the traditional quantum mechanics which assume—in contrast and as a consequence of Heisenberg’s uncertainty principle—electronic probabilities of presence. Its basic idea consists of the assumption that the motions of the two electrons are influenced by their spins exhibiting the value h/2π, but in two different ways: on the one hand, one spin induces a rotation;and on the other hand, the other spin induces a harmonic oscillation. A second important relation is given by the fact that the retroactive force of the oscillation process is due to the centrifugal force when the process runs along the surface of a sphere, whereas in usual oscillation processes—such as the one of a spring pendulum—it is due to a permanent shift between potential and kinetic energy. Therefore, in the present case, the potential energy remains constant since the distance between the nucleus and the—diametrically positioned—electrons remains constant. Considering these two conditions and the usual physical relations such as Coulomb attraction, centrifugal force, and the conservation laws of the angular momentum and of the energy, it was possible to compute the respective key values. Thereby, the deflection of the oscillation angle ψ = 45˚is remarkable. Finally, the process is described using a Cartesian coordinate system with z as the rotation axis, a variable oscillation distance d and variable rotation velocities r<sub>rot</sub>. Thereby, the projections onto the x-axis and on the y-axis are not identically equal, leading to an elliptic projection shape. Thus this system is anisotropic, in contrast to the isotropic array of the conventional quantum mechanics according to Schrödinger, where the 1s-orbital is spherically symmetrical. This anisotropy explains the existence of interatomic Van der Waals forces, which enable the condensation of Helium, even though the condensation temperature is very low. But in particular, it exhibits well-defined electron waves, thus finally delivering the explanation of the hypothesis of Louis de Broglie, which has been established 100 years ago.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 present approach is an advancement of the author’s former attempts to develop an atom model of Helium with well-defined electron trajectories. Thus it calls in question the traditional quantum mechanics which assume—in contrast and as a consequence of Heisenberg’s uncertainty principle—electronic probabilities of presence. Its basic idea consists of the assumption that the motions of the two electrons are influenced by their spins exhibiting the value h/2π, but in two different ways: on the one hand, one spin induces a rotation;and on the other hand, the other spin induces a harmonic oscillation. A second important relation is given by the fact that the retroactive force of the oscillation process is due to the centrifugal force when the process runs along the surface of a sphere, whereas in usual oscillation processes—such as the one of a spring pendulum—it is due to a permanent shift between potential and kinetic energy. Therefore, in the present case, the potential energy remains constant since the distance between the nucleus and the—diametrically positioned—electrons remains constant. Considering these two conditions and the usual physical relations such as Coulomb attraction, centrifugal force, and the conservation laws of the angular momentum and of the energy, it was possible to compute the respective key values. Thereby, the deflection of the oscillation angle ψ = 45˚is remarkable. Finally, the process is described using a Cartesian coordinate system with z as the rotation axis, a variable oscillation distance d and variable rotation velocities r<sub>rot</sub>. Thereby, the projections onto the x-axis and on the y-axis are not identically equal, leading to an elliptic projection shape. Thus this system is anisotropic, in contrast to the isotropic array of the conventional quantum mechanics according to Schrödinger, where the 1s-orbital is spherically symmetrical. This anisotropy explains the existence of interatomic Van der Waals forces, which enable the condensation of Helium, even though the condensation temperature is very low. But in particular, it exhibits well-defined electron waves, thus finally delivering the explanation of the hypothesis of Louis de Broglie, which has been established 100 years ago.
