Related papers: One-dimensional quantum scattering by a parabolic …
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
The goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials. The asymptotic nature…
We show that Wronskians between properly chosen linearly independent solutions of the Schr\"odinger equation greatly facilitate the study of quantum scattering in one dimension. They enable one to obtain the necessary relationships between…
Recently, in Quantum Field theory, there has been an interest in scattering in highly singular potentials. Here, solutions to the stationary Schroedinger equation are presented when the potential is a multiple of an arbitrary positive power…
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…
In this paper we consider an inverse problem for the $n$-dimensional random Schr\"{o}dinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a Gaussian random…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the…
We study one-dimensional scattering for a decaying potential with rapid periodic oscillations and strong localized singularities. In particular, we consider the Schr\"odinger equation \[ H_\epsilon \psi := (-\partial_x^2 + V_0(x) +…
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…
We prove that the inverse scattering problem for the Schr\"odinger operator with the separable potential can be reduced to the solving of a certain singular integral equation. We establish the uniqueness of the potential corresponding to…