Related papers: Wave function as geometric entity
The quantum molecule consisting of three quantum dots that forms a triangle with its centers is studied. The electron wave function in the nanosystem is written using the linear combination of orbital quantum wells. The dispersion equation…
It is well known that Schr\"{o}dinger's equation is only suitable for the particle in conservative force field. In atomic and molecular field, a particle can suffer the action of non-conservative force. In this paper, a new quantum wave…
Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate the combined effects of the geometry of…
Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics…
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
Electrons in solids are characterized by the energy bands, which indicate that electrons are considered to be "elementary particles" with specific effective masses and g-factors reflecting features of each solid. There are cases where these…
Following de Broglie and Vigier, a fully relativistic causal interpretation of quantum mechanics is given within the context of a geometric theory of gravitation and electromagnetism. While the geometric model shares the essential…
One of the major concerns of Schr\"odinger, Lorentz, Einstein, and many others about the wave function is that it is defined on the $3\mathbf{N}$-dimensional configuration space, rather than on the $3$-dimensional physical space. This gives…
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
The quantum field of a single particle is expressed as the sum of the particle's ordinary wave function and the vacuum fluctuations. An exact quantum-field calculation shows that the squared amplitude of this field sums, at any time, to a…
Stationary electromagnetic waves display aspects that are shared with massive particles, since the energy and momentum contained in a volume of sides equal to the wavelengths form a non-zero energy-momentum invariant. The parallel can be…
The wave-structure of moving electrons is analyzed on a fundamental level by employing a modified de Broglie relation. Formalizing the wave-function $\psi$ in real notation yields internal energy components due to mass oscillations. The…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
Scattering of electromagnetic (EM) waves by many small particles (bodies), embedded in a thin layer, is studied. Physical properties of the particles are described by their boundary impedances. The thin layer of depth of the order $O(a)$…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical…
We generalize Bohr's complementarity principle for wave and particle properties to arbitrary quantum systems. We begin by noting that a particle-like state is represented by a spatially-localized wave function and its narrow probability…
The solution of Dirac's equation for the hydrogen atom according to relativistic wave mechanics yields for each state a vectorial amplitude function with four components, two large and two small. Each such component has its characteristic…
The Compton effect is commonly cited as a demonstration of the particle feature of light, while the wave nature of matter has been proposed by de Broglie and demonstrated by Davisson and Germer with the Bragg diffraction of electron beams.…