Related papers: Localized Beams and Dielectric Barriers
Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional…
Special relativity combined with the stochastic vacuum flux impact model lead to an explicit interpretation of many of the phenomena of elementary quantum mechanics. We examine characteristics of a repetitively impacted submicroscopic…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…
Similarities between quantum systems and analogous systems for classical waves have been used to great effect in the physics community, be it to gain an intuition for quantum systems or to anticipate novel phenomena in classical waves. This…
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 study the effect of a $\delta$ distribution potential placed at $x_0\geq 0$ and multiplied by a parameter $\alpha$ on a quantum mechanical particle in an infinite square well over the segment $\left[-\,\frac{L}{2},\frac{L}{2}\right]$. We…
We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schr{\"o}dinger equation, which goes beyond the standard semi-classical…
In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…
We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…
The parametric ladder climbing (successive Landau-Zener-type transitions) and the quantum saturation of the threshold for the classical parametric autoresonance due to the zero point fluctuations at low temperatures are discussed. The…
Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are…
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
The solution of the time-dependent Schr\"odinger equation is discussed for a particle confined in half-space $x>0$ with a linear potential $V(x)=Kx$ in the following situations: (a) sudden removal of the wall and switching on the linear…
The standard derivation of Schroedinger's equation from a Lorentz-invariant Feynman path integral consists in taking first the limit of infinite speed of light and then the limit of short time slice. In this order of limits the light cone…
Time double-slit interference experiments have been achieved and presented as complementary to spatial double-slit interference experiments, providing a further confirmation of the wave-particle duality. Numerical solutions of the free…
The effect of the thickness of the dielectric boundary layer that connects a material of refractive index $n_1$ to another of index $n_2$ is considered for the propagation of an electromagnetic pulse. For very thin boundary layer the…
The theoretical foundations of quantum mechanics and de Broglie--Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal…
In order to settle the problem of the "Post constraint" in material media, we consider the propagation of a plane electromagnetic wave in a medium with a piecewise constant axion field. Although a constant axion field does not affect the…
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale…