Related papers: Scattering by a toroidal coil
In this paper we find a new condition on a real periodic potential for which the self-adjoint Schr\"odinger operator may be defined by a quadratic form and the spectrum of the operator is purely absolutely continuous. This is based on…
Stationary scattering problem (when the distance $r$ tends to infinity) and dynamical scattering problem (when the time $t$ tends to infinity) are considered for the 3D Schr\"odinger equation. A simple interconnection between the scattering…
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In previous papers, we proved the existence of modified wave operators for…
The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complimentary situations, firstly when the…
We consider the Schr\"odinger operator ${\bf H}=(i\nabla+A)^2 $ in the space $L_2({\mathbb R}^3)$ with a magnetic potential $A $ created by an infinite straight current. We perform a spectral analysis of the operator ${\bf H}$ almost…
In this paper, we prove the existence of the scattering operator for the fractional magnetic Schrodinger operators. For this, we construct the fractional distorted Fourier transforms with magnetic potentials. Applying the properties of the…
We study scattering for the couple $(A_{F},A_{0})$ of Schr\"odinger operators in $L^2(\mathbb{R}^3)$ formally defined as $A_0 = -\Delta + \alpha\, \delta_{\pi_0}$ and $A_F = -\Delta + \alpha\, \delta_{\pi_F}$, $\alpha >0$, where…
We study the theory of scattering for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling,in space dimension 3.We prove in particular the existence of modified wave operators for that system with…
Explicit formulas for the analytic extensions of the scattering matrix and the time delay of a quasi-one-dimensional discrete Schr\"odinger operator with a potential of finite support are derived. This includes a careful analysis of the…
We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…
The scattering matrix of the Schrodinger operator with smooth short-range electric and magnetic potentials is considered. The asymptotic density of the eigenvalues of this scattering matrix in the high energy regime is determined. An…
We consider the cubic nonlinear Schr\"odinger equation posed on the spatial domain $\mathbb{R}\times \mathbb{T}^d$. We prove modified scattering and construct modified wave operators for small initial and final data respectively ($1\leq…
Exact solutions of the Schr\"odinger equation for the Coulomb potential are used in the scope of both stationary and time-dependent scattering theories in order to find the parameters which define regularization of the Rutherford…
We study an inverse scattering problem at fixed energy for radial magnetic Schr{\"o}dinger operators on R^2 \ B(0, r\_0), where r\_0 is a positive and arbitrarily small radius. We assume that the magnetic potential A satisfies a gauge…
We consider the Schr\"odinger operator in ${\mathbb R}^n$, $n\geq 3$, with the electric potential $V$ and the magnetic potential $A$ being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
When the Schr\"{o}dinger equation for stationary states is studied for a system described by a central potential in $n$-dimensional Euclidean space, the radial part of stationary states is an even function of a parameter $\lambda$ which is…
The study of obstacle scattering for the Klein-Gordon equation in the presence of long-range magnetic potentials is addressed. Previous results of the authors are extended to the long-range case and the results the authors previously proved…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
We study the scattering properties of Schr\"{o}dinger operators with potentials that have short-range decay along a collection of rays in $\bbR^d$. This generalizes the classical setting of short-range scattering in which the potential is…