Related papers: Wave function as geometric entity
Waves play an essential role in many aspects of plasma science, such as plasma manipulation and diagnostics. Due to the complexity of the governing equations, approximate models are often necessary to describe wave dynamics. In this…
Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.
This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object,…
The explanation of the photoelectric effect by Einstein and Maxwell's field theory of electromagnetism have motivated De Broglie to make the hypothesis that matter exhibits both waves and particles like-properties. These representations of…
By viewing the electron as a wavepacket in the positive energy spectrum of the Dirac equation, we are able to achieve a much clearer understanding of its behavior under weak electromagnetic fields. The intrinsic spin magnetic moment is…
Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities,…
This study investigates the interaction of a shock wave with a fixed layer of particles in cylindrical geometries using particle-resolved large eddy simulations. The curvature radius of the particle layer is varied and the resulting flow…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry…
An electron behaves as both a particle and a wave. On account of this it can be controlled in a similar way to a photon and electronic devices can be designed in analogy to those based on light when there is minimal excitation of the…
This is an attempt to construct a classical microscopic model of the electron which underlies quantum mechanics. An electron is modeled, not as a point particle, but as the end of an electromagnetic string, a line of flux. These lines…
Relations between particle and wave properties for charge carriers in periodic potentials of crystalline metals and semiconductors are derived. The particle aspects of electrons and holes in periodic potentials are considered using…
It is shown that `bipartite' wave functions can present a mathematical formalism of quantum theory for a single particle, in which the associated Schr\"{o}dinger's wave functions correspond to those `bipartite' wave functions of product…
Partial solutions of the Dirac equation describing an electron motion in electromagnetic crystals created by plane waves with linear and circular polarizations are treated. It is shown that the electromagnetic crystal formed by circularly…
Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…
The existence of twisted light may be inferred from modern quantum concepts and experimental data. These waves possess energy, impulse and angular momentum. However, the Maxwell's four-dimensional theory of electromagnetism does not imply…
An differential equation for wave functions is proposed, which is equivalent to Schr\"{o}dinger's wave equation and can be used to determine energy-level gaps of quantum systems. Contrary to Schr\"{o}dinger's wave equation, this equation is…
The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…