Related papers: Perturbative solution approach for computing the t…
We propose two stable and one conditionally stable finite difference schemes of second-order in both time and space for the time-fractional diffusion-wave equation. In the first scheme, we apply the fractional trapezoidal rule in time and…
In this paper, we study the light double-slit diffraction experiment with quantum theory approach. Firstly, we calculate the light wave function in slits by quantum theory of photon. Secondly, we calculate the diffraction wave function with…
The problem of diffraction of an electromagnetic plane wave by a perfectly conducting circular disk and its complementary problem, diffraction by a circular hole in an infinite conducting plate, are rigorously solved using the method of the…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
We present a simple method to include the effects of diffraction into the description of a light-atomic ensemble quantum interface in the context of collective variables. Carrying out a scattering calculation we single out the purely…
We investigate the radiation emitted by an ultrarelativistic electron traveling in a 1-dimensional parabolic potential. Having in mind a simplified model for beamstrahlung, we consider the realistic case of the electron motion being highly…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
In recent years, an extensive survey on various wave equations of relativistic quantum mechanics with different types of potential interactions has been a line of great interest. In this regime, special attention has been given to the Dirac…
Periodically driven systems can host many interesting and intriguing phenomena. The irradiated two-dimensional Dirac systems, driven by circularly polarized light, are the most attractive thanks to intuitive physical view of the absorption…
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…
The main objective of this work is to present a theoretical proposal for an implementation of the $(2 + 1)$-dimensional Dirac equation in classical gravitational and electromagnetic backgrounds in a two-dimensional waveguide array. For…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
The Dirac equation is used to describe oblique spin-conserving and spin-flip reflections of relativistic electrons from a one-dimensional potential barrier in a vacuum. When an electron hits the barrier from an oblique direction, its…
We investigate the effects of spin-momentum locking on the interference and diffraction patterns due to a double- or single-slit in an electronic \emph{Gedankenexperiment}. We show that the inclusion of the spin-degree-of-freedom, when…
The aim of this Note is to prove by a perturbation method the existence of solutions of the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state and with the…
The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…
The Green function (GF) related to the problem of a Dirac particle interacting with a plane wave and constant magnetic fields is calculated in the framework of path integral via Alexandrou et al. formalism according to the so-called global…
We advance a new analytical method for the Dirac equation in two-dimensional, homogeneous, time-dependent electric fields, which expresses the Cauchy problem of the two-component spinor and its derivative as the time-ordered integral of the…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
The time-dependence of the Bragg diffraction by one-dimensional photonic crystals and its influence on the short pulse reflection are studied in the framework of the coupled- wave theory. The indicial response of the photonic crystal is…