71 citations · 537 across the 49 of their papers we have counts for
32 papers · 1 filter
Factorization for the full-line matrix Schrödinger equation and a unitary transformation to the half-line scattering
Tuncay Aktosun, Ricardo Weder
The scattering matrix for the full-line matrix Schrödinger equation is analyzed when the corresponding matrix-valued potential is selfadjoint, integrable, and has a finite first mo…
The boundedness of the wave operators for matrix Schrödinger equations
Ricardo Weder
We prove that the wave operators for matrix Schrödinger equations on the half line, with general selfadjoint boundary condition, are bounded in the spaces $L^p(\mathbb…
estimates for matrix Schrödinger equations
Ivan Naumkin, Ricardo Weder
This paper is devoted to the study of dispersive estimates for matrix Schrödinger equations on the half-line with general boundary condition, and on the line. We prove $L^{p}-L^{p^…
Inverse scattering on the half line for the matrix Schrödinger equation
Tuncay Aktosun, Ricardo Weder
The matrix Schrödinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain a…
The Inverse Scattering Problem for the Matrix Schrödinger Equation
Tuncay Aktosun, Ricardo Weder
The matrix Schrödinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain a…
The number of eigenvalues of the matrix Schrödinger operator on the half line with general boundary conditions
Ricardo Weder
We prove a bound, of Bargmann- Birman-Schwinger type, on the number of eigenvalues of the matrix Schrödinger operator on the half line, with the most general self adjoint boundary…
Trace Identities for the matrix Schrödinger operator on the half line with general boundary conditions
Ricardo Weder
We prove Buslaev-Faddeev trace identities for the matrix Schrödinger operator on the half line, with general boundary conditions at the origin, and with selfadjoint matrix potentia…
Time delay for the Dirac equation
Ivan Naumkin, Ricardo Weder
We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator $\int\limits_{0} ^{\infty}e^{iH_{0}t}ζ\left( \fra…
Aharonov-Bohm Effect and High-Momenta Inverse Scattering for the Klein-Gordon Equation
Miguel Ballesteros, Ricardo Weder
We analyze spin-0 relativistic scattering of charged particles propagating in the exterior, , of a compact obstacle . The connected c…
High-Momenta Estimates for the Klein-Gordon Equation: Long-Range Magnetic Potentials and Time-Dependent Inverse Scattering
Miguel Ballesteros, Ricardo Weder
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 l…
Scattering Theory for the matrix Schrödinger operator on the half line with general boundary conditions
Ricardo Weder
We study the stationary scattering theory for the matrix Schrödinger equation on the half line, with the most general boundary condition at the origin, and with integrable selfadjo…
High-Velocity Estimates for Schrödinger Operators in Two Dimensions: Long-Range Magnetic Potentials and Time-Dependent Inverse Scattering
Miguel Ballesteros, Ricardo Weder
We introduce a general class of long-range magnetic potentials and derive high velocity limits for the scattering operators in quantum mechanics, in the case of two dimensions. We…
High-energy and smoothness asymptotic expansion of the scattering amplitude for the Dirac equation and applications
Ivan Naumkin, Ricardo Weder
We obtain an explicit formula for the diagonal singularities of the scattering amplitude for the Dirac equation with short-range electromagnetic potentials. Using this expansion we…
Small-energy analysis for the selfadjoint matrix Schroedinger operator on the half line. II
Tuncay Aktosun, Martin Klaus, Ricardo Weder
The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the mat…
High-Energy analysis and Levinson's theorem for the selfadjoint matrix Schroedinger operator on the half line
Tuncay Aktosun, Ricardo Weder
The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the general selfadjoint boundary condition at the origin. When the matrix p…
On Open Scattering Channels for Manifolds with Ends
Rainer Hempel, Olaf Post, Ricardo Weder
In the framework of time-dependent geometric scattering theory, we study the existence and completeness of the wave operators for perturbations of the Riemannian metric for the Lap…
Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line
Tuncay Aktosun, Martin Klaus, Ricardo Weder
The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the mat…
High-Velocity Estimates and Inverse Scattering for Quantum N-Body Systems with Stark Effect
Gerardo Daniel Valencia, Ricardo Weder
In an N-body quantum system with a constant electric field, by inverse scattering, we uniquely reconstruct pair potentials, belonging to the optimal class of short-range potentials…
The Electric Aharonov-Bohm Effect
Ricardo Weder
In their seminal paper Aharonov and Bohm (1959) claimed that electromagnetic fields can act at a distance on charged particles even if they are identically zero in the region of sp…
Aharonov-Bohm Effect and High-Velocity Estimates of Solutions to the Schrödinger Equation
Miguel Ballesteros, Ricardo Weder
The Aharonov-Bohm effect is a fundamental and controversial issue in physics. At stake are what are the fundamental electromagnetic quantities in quantum physics, if magnetic field…
Analysis of Acoustic Wave Propagation in a Thin Moving Fluid
Patrick Joly, Ricardo Weder
We study the propagation of acoustic waves in a fluid that is contained in a thin two-dimensional tube, and that it is moving with a velocity profile that only depends on the trans…
The Aharonov-Bohm Effect and Tonomura et al. Experiments. Rigorous Results
Miguel Ballesteros, Ricardo Weder
We study the Aharonov-Bohm effect under the conditions of the Tonomura et al. experiments, that gave a strong evidence of the physical existence of the Aharonov-Bohm effect, and we…
High-Velocity Estimates for the Scattering Operator and Aharonov-Bohm Effect in Three Dimensions
Miguel Ballesteros, Ricardo Weder
We obtain high-velocity estimates with error bounds for the scattering operator of the Schrödinger equation in three dimensions with electromagnetic potentials in the exterior of b…
Inverse Scattering at a Fixed Energy for Long-Range Potentials
Ricardo Weder, Dimitri Yafaev
In this paper we consider the inverse scattering problem at a fixed energy for the Schrödinger equation with a long-range potential in $\ere^d, d\geq 3$. We prove that the long-ran…