Related papers: More on some non-gaussian wave packets
Using the Caldirola-Kanai Hamiltonian, we study the time evolution of the wave function of a particle whose classical motion is governed by the Langevin equation. We show, in particular, that if the initial wave function is Gaussian, then…
This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper…
General relativity describes the dynamics of gravitational waves, which can feature nonlinear interactions, such as those underlying turbulent processes. Theoretical and numerical explorations have demonstrated the existence of…
According to electrodynamical equations in curved spacetime we consider the coupling of a linearized weak gravitational wave (GW) to a Gaussian beam passing through a static magnetic field. It is found that unlike the properties of the…
A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular…
In a two-dimensional approximation, the probability density and current for a photoelectron near the localization of a quantum vortex are theoretically investigated. The wave function in the momentum representation, which we found earlier,…
We generalize our previous linear result [1] in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly…
We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusive spectral stability assumption and prove that it implies…
The energy content of cylindrical gravitational wave spacetimes is analyzed by considering two local descriptions of energy associated with the gravitational field, namely those based on the C-energy and the Bel-Robinson super-energy…
We discuss the semi-classical gravitational wave corrections to Gauss's law, and obtain an explicit solution for the electromagnetic potential. The Gravitational Wave perturbs the Coulomb potential with a function which propagates to the…
We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…
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…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
We present a wave packet analysis of a class of possibly degenerate parabolic equations with variable coefficients. As a consequence, we prove local wellposedness of the corresponding Cauchy problem in spaces of low regularity, namely the…
Two concepts of plane waves in anisotropic viscoelastic media are studied. One of these concepts allows for the use of methods based on the theory of complete Bernstein functions. This allows for a deeper study of frequency-domain…
Cylindrically symmetric analogue of the Volkov problem is examined. In presence of the field of a cylindrical electromagnetic wave, classical motion of a non-relativistic particle on a cylindrical surface is described exactly in terms of…
In this article we present an exact and unified description of wave-packet dynamics in various 2D systems in presence of a transverse magnetic field. We consider an initial minimum-uncertainty Gaussian wave-packet, and find that its long…
We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used…
We obtain a new family of exact vacuum solutions to quadratic gravity that describe pp-waves with two-dimensional wave surfaces that can have any prescribed constant curvature. When the wave surfaces are flat we recover the Peres waves…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…