Related papers: Objective Reality of de Broglie's Waves
Is the wave function a physical reality traveling through our apparatus? Is it a real wave, or it is only a mathematical tool for calculating probabilities of results of measurements? Different interpretations of the quantum mechanics (QM)…
Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic wave problems, as their trial spaces contain…
We present a wave generalization of the classic Schwarzschild method for constructing self-consistent halos -- such a halo consists of a suitable superposition of waves instead of particle orbits, chosen to yield a desired mean density…
The coherent propagation of elastic waves in a solid filled with a random distribution of pinned dislocation segments is studied to all orders in perturbation theory. It is shown that, within the independent scattering approximation, the…
Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…
It is hypothesized that de Broglie's 'matter waves' provide a dynamical basis for Minkowski spacetime in an antisubstantivalist or relational account. The relativity of simultaneity is seen as an effect of the de Broglie oscillation…
We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction…
Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small…
A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
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…
Two approaches to solution of the two-dimensional Helmholtz equation with a "wave number" are proposed. The results can be applied both in numerical areas of physics and in the theory of nonlinear equations. The first approach is based on…
This paper concerns the study and resolution of wave equations in the space of Schwartz distributions. Wave phenomena are widespread in many branches of physics and chemistry, such as optics, gravitation, quantum mechanics, chemical waves…
In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein-Gordon and Dirac equations in Rindler coordinates with…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
We construct deterministic solutions to the Helmholtz equation in $\mathbb{R}^m$ which behave accordingly to the Random Wave Model. We then find the number of their nodal domains, their nodal volume and the topologies and nesting trees of…
We investigate elliptic fractional equations in the whole space, involving zero order perturbations of the fractional Laplacian $(-\Delta)^s$, $0<s<1$. Our main objective is to determine appropriate radiation conditions at infinity that…
An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic…
The interpretation proposed in quant-ph/9812011 is extended to the general case of a non-relativistic particle moving in an arbitrary external potential. It is shown that, even in this general case, "particle" solutions exist which do not…
We present a geometric optics theory for the transport of quantum particles (or classical waves) in a chiral and dissipative periodic crystal subject to slowly varying perturbations in space and time. Taking account of some properties of…