2017.11.28 GIF- portrait of an electron. (original) (raw)
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The wave function of the internal state of the electron
An attempt to reverse-engineer the wave function of the internal state of the electron from its properties leads to proposals of answers about forces stabilizing the electron and an electromagnetic input to its annihilation energy.
4. Wave Solution of Generalized Maxwell Equations and Quantum Mechanics
Let us summarize the main results. The wave solution for the Generalized Maxwell equations led us to the concept of the wave created by a moving electron as an essentially three-dimensional torsional oscillation. This oscillation takes place in longitudinal (along speed) and transverse (perpendicular) directions. This oscillation defines a traveling wave with amplitudes in longitudinal and transverse directions that are connected. Therefore, suppression of oscillation in one direction leads to suppression of oscillation in the other direction. In addition to this two-dimensional oscillation, the electron’s wave oscillates in the third dimension creating a standing wave independent with respect to time and the electron’s own movement, in contrast to the above mentioned-traveling wave. This standing wave defines the electron’s charge and Coulomb interaction force with other charges. Therefore the Coulomb force turns to be a long range one, in contrast to the Lorentz force, which is defined by a traveling wave that moves with electron’s velocity. One can say this in another way. The wave creating Coulomb force exists I ether from time immemorial. But the generalized Lorentz force is generated by movement and disappears with it. A positron possesses a similar standing wave with opposite sign. In an electron-positron collision, the standing waves are mutually annihilated, which means charge annihilation. These waves can appear only being “repulsed” by each other. Therefore electric charges appear only in couples: positive and negative ones. A certain visual notion about the electron as a massive torus rotating in equatorial and meridional planes is proposed. Charge magnitude is defined by the electron’s mass and the angular velocity of its equatorial rotation. If it constitutes right hand screw with meridional angle velocity, one gets charge of one sign, and of opposite sign in the opposite case. This screw also defines the sign of the above-mentioned standing wave.
Applied Physics Research, 2019
An electron model is developed based on a 4D sphere with a diameter of the Planck length. This model allows us to explain and calculate the intrinsic properties of the electron, such as its mass, charge, spin, etc., from the fundamental constants. Using this Planck sphere in four dimensions, we reach the conclusion that the electron particle has a size that is fixed by the Planck dimensions. The rotation of the Planck sphere generates the electron wave, the size of which depends on its wavelength. Our hypothesis is that the universe is composed of Planck spheres in four spatial dimensions, with two possible states: a rest state and rotational movement.
Properties of the two-dimensional electron gas
Journal of Molecular Structure: THEOCHEM, 1999
ABSTRACT Ground state properties of the two-dimensional electron gas are studied in the deformable jellium model. The calculations are made within the self-consistent Hartree–Fock approximation. The phase transition from plane wave solutions to the corrugated state (Wigner like transition) is analysed for two different crystallographic symmetries. A comparison of the results in the cases studied is presented. The behaviour of the energy curve is studied for a wide range of densities. Our calculations of the melting point are within an order of magnitude of experimental data.
Journal of Modern Physics, 2015
Following Ashcroft and Mermin, the conduction electrons ("electrons" or "holes") are assumed to move as wave packets. Dirac's theorem states that the quantum wave packets representing massive particles always move, following the classical mechanical laws of motion. It is shown here that the conduction electron in an orthorhombic crystal moves classical mechanically if the primitive rectangular-box unit cell is chosen as the wave packet, the condition requiring that the particle density is constant within the cell. All crystal systems except the triclinic system have k-vectors and energy bands. Materials are conducting if the Fermi energy falls on the energy bands. Energy bands and gaps are calculated by using the Kronig-Penny model and its 3D extension. The metal-insulator transition in VO2 is a transition between conductors having three-dimensional and one-dimensional k-vectors.
The topological features of the intracule density of the uniform electron gas
Chemical Physics Letters, 1999
The Laplacian of the self-consistent-field radial intracule density of the uniform electron gas has been analyzed. It reaches its absolute maximum at the electron-electron coalescence point with a value of 0.3r 2 , where r is the electron charge density. Then, it decreases as the interlectronic distance increases and has an attenuated oscillatory decay at larger distances. Further examination of this function yields an onion-like representation of the spatial structure of the uniform electron gas from the viewpoint of an arbitrary reference electron. Our calculations demonstrate that the radius of the first layer is 13.069r and the remaining layers obey a simple relationship with respect to the layer number with a separation of s 6.065r between adjacent layers. q
Standing Waves of an electron in Hydrogen Atom
The electron of an Hydrogen atom, orbits the nucleus in discrete orbits as described by the Bohr model. But we know from the theory proposed by de Broglie in 1925, that all particles of matter can be associated with a certain matter wave. So the electron orbiting the nucleus also has this wave nature. In fact the electron in a given orbit can be looked as a standing wave. In this paper we shall analyze the normal modes of the standing wave of the electron, justify Bohr's second postulate and also show how we can transform the Bohr model of hydrogen atom into the Quantum model that we are familiar with today.
A physical model of the electron according to the Basic Structures of Matter Hypothesis
Physics Essays, 2003
A physical model of the electron is suggested according to the basic structures of matter (BSM) hypothesis. BSM is based on an alternative concept about the physical vacuum, assuming that space contains an underlying grid structure of nodes formed of superdense subelementary particles, which are also involved in the structure of the elementary particles. The proposed grid structure is formed of vibrating nodes that possess quantum features and energy well. It is admitted that this hypothetical structure could account for the missing "dark matter" in the universe. The signature of this dark matter is apparent in the galactic rotational curves and in the relation between masses of the supermassive black hole in the galactic center and the host galaxy. The suggested model of the electron possesses oscillation features with anomalous magnetic moment and embedded signatures of the Compton wavelength and the fine-structure constant. The analysis of the interactions between the oscillating electron and the nodes of the vacuum grid structure allows us to obtain physical meaning for some fundamental constants.
Hydrodynamic model for 2D degenerate free-electron gas for arbitrary frequencies
Revista Mexicana De Fisica - REV MEX FIS, 2003
Recibido el 9 de julio de 2002; aceptado el 31 de enero de 2003 Following Halevi's procedure for 3D degenerate free-electron gas (3D-DEG), we investigate the response function in the hydrodynamic model (HM) for 2D-DEG confined in low dimensional systems when collisions are included. For small wavevectors we found from the twodimensional Boltzmann-Mermin model a useful expression for the HM complex stiffness parameter of the nonlocal dielectric function β, which is β 2 = [((3ω/4) + i(ν/2)) /(ω + iν)]v 2 F , where ω and ν are the circular and collisional frequencies and vF is the Fermi velocity. Keywords: Theories and models of many-electron systems; optical properties of low dimensional materials; theory of electronic transport; scuttering mechanisms. Siguiendo el procedimiento de Halevi para un gas libre degenerado de electrones en 3D (3D-GED), investigamos la función de respuesta en el modelo hidrodinámico (MH) de un 2D-GED confinado en sistemas de baja dimensionalidad cuando las colisiones son incluidas. Utilizando el modelo bidimensional de Boltzmann-Mermin, encontramos en el MH para vectores de onda pequeños una expresiónútil para el parámetro de rigidez complejo de la función dieléctrica no local β, la cual es β 2 = [((3ω/4) + i(ν/2)) /(ω + iν)]v 2 F , donde ω y ν son las frecuencias circular y de colisión y vF es la velocidad de Fermi. Descriptores: Teoría y modelos de sistemas de muchos electrones; propiedadesópticas de materiales de baja dimensionalidad; teoría de transporte electrónico; mecanismos de dispersión.
Electron-acoustic solitary waves in the presence of a suprathermal electron component
Physics of Plasmas, 2011
The nonlinear dynamics of electron-acoustic localized structures in a collisionless and unmagnetized plasma consisting of "cool" inertial electrons, "hot" electrons having a kappa distribution, and stationary ions is studied. The inertialess hot electron distribution thus has a long-tailed suprathermal (non-Maxwellian) form. A dispersion relation is derived for linear electron-acoustic waves. They show a strong dependence of the charge screening mechanism on excess suprathermality (through \kappa). A nonlinear pseudopotential technique is employed to investigate the occurrence of stationary-profile solitary waves, focusing on how their characteristics depend on the spectral index \kappa, and the hot-to-cool electron temperature and density ratios. Only negative polarity solitary waves are found to exist, in a parameter region which becomes narrower as deviation from the Maxwellian (suprathermality) increases, while the soliton amplitude at fixed soliton speed increases. However, for a constant value of the true Mach number, the amplitude decreases for decreasing \kappa.