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  1. 手机体育投注平台 Book Series

    Applied Mathematical Sciences

    Volume 1 / 1971 to Volume 204 / 2020

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    Book

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    Chapter

    The Matrix Schrödinger Equation and the Characterization of the Scattering Data

    In this chapter we describe the basic ingredients of the direct and inverse scattering problems for the matrix Schrödinger equation on the half line with the general self-adjoint boundary condition. We show ho...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    Chapter

    Direct Scattering II

    手机体育投注平台 In this chapter the scattering process is described physically and mathematically, and the definition of the scattering operator is provided in terms of the wave operators introduced by Møller. The role of the...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    Chapter

    Some Explicit Examples

    手机体育投注平台 In this chapter we illustrate the theory presented earlier via explicitly solved examples. It is shown how the Marchenko integral equation can yield explicitly solved examples when its kernel contains a matrix...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    手机体育投注平台 Chapter

    Introduction

    In this introductory chapter the goals of the monograph are described, the contents of the remaining chapters and Appendix A手机体育投注平台 are outlined, and the relevant general refer...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    手机体育投注平台 Chapter

    Direct Scattering I

    In this chapter we present the solution to the direct scattering problem for the half-line matrix Schrödinger equation using an input data set consisting of a matrix potential and a self-adjoint boundary condi...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    手机体育投注平台 Chapter

    Inverse Scattering

    In this chapter we analyze the inverse scattering problem of recovery of the corresponding input data set D in the Faddeev class from a scattering data set S in the Marchenko class. We discuss the nonuniqueness a...

    Tuncay Aktosun, Ricardo Weder in Direct and Inverse Scattering for the Matr… (2021)

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    Article

    \(L^{p}-L^{p^{\prime }}\) estimates for matrix Schrödinger equations

    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 \(L^{p}-L^{p^{\prime }}\) L p - L p ′

    Ivan Naumkin, Ricardo Weder in Journal of Evolution Equations (2020)

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    手机体育投注平台 Article

    Time Delay for the Dirac Equation

    We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator $${...

    Ivan Naumkin, Ricardo Weder in Letters in Mathematical Physics (2016)

  11. Article

    Aharonov–Bohm Effect and High-Momenta Inverse Scattering for the Klein–Gordon Equation

    We analyze spin-0 relativistic scattering of charged particles propagating in the exterior, \({\Lambda \subset \mathbb{R}^3}\) ...

    Miguel Ballesteros, Ricardo Weder in Annales Henri Poincaré (2016)

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    手机体育投注平台 Article

    Aharonov-Bohm Effect and High-Velocity Estimates of Solutions to the Schrödinger Equation

    The Aharonov-Bohm effect is a fundamental issue in physics that has been extensively studied in the literature and is discussed in most of the textbooks in quantum mechanics. The issues at stake are what are t...

    Miguel Ballesteros, Ricardo Weder in Communications in Mathematical Physics (2011)

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    Article

    High-Velocity Estimates for the Scattering Operator and Aharonov-Bohm Effect in Three Dimensions

    手机体育投注平台 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 bounded obstacles that are han...

    Miguel Ballesteros, Ricardo Weder in Communications in Mathematical Physics (2009)

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    手机体育投注平台 Article

    The Two-Spectra Inverse Problem for Semi-infinite Jacobi Matrices in The Limit-Circle Case

    We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditio...

    Luis O. Silva, Ricardo Weder in Mathematical Physics, Analysis and Geometry (2008)

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    Article

    On the Two Spectra Inverse Problem for Semi-infinite Jacobi Matrices

    We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg–Marchenko t...

    Luis O. Silva, Ricardo Weder in Mathematical Physics, Analysis and Geometry (2006)

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    Chapter and Conference Paper

    Time-Dependent Methods in Inverse Scattering Theory

    The time-dependent approach to inverse scattering theory is discussed and the cases of potential scattering and of the nonlinear Schrödinger equation with a potential are studied in detail. We give a time-depe...

    Ricardo Weder in New Analytic and Geometric Methods in Inverse Problems (2004)

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    Chapter and Conference Paper

    The Time-Dependent Approach to Inverse Scattering

    手机体育投注平台 In this talk we present a time-dependent approach for the solution of inverse scattering problems. With our approach we prove uniqueness and we give a method for the reconstruction of the potentials. This appr...

    Ricardo Weder in Partial Differential Equations and Spectral Theory (2001)

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    Article

    Center Manifold for Nonintegrable Nonlinear Schrödinger Equations on the Line

    In this paper we study the following nonlinear Schrödinger equation on the line,

    Ricardo Weder in Communications in Mathematical Physics (2000)

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    Article

    The W k, p -Continuity of the Schrödinger Wave Operators on the Line

    We prove that the wave operators for the Schrödinger equation on the line are continuous on the Sobolev spaces W k, p , 1 < p手机体育投注平台 < ∞. Moreover, if the pote...

    Ricardo Weder in Communications in Mathematical Physics (1999)

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    Chapter and Conference Paper

    Inverse scattering for N-body systems with time-dependent potentials

    手机体育投注平台 I prove that the high velocity limit of any one of the Dollard scattering operators of an N-body quantum mechanical system with long-range time-dependent pair potentials determines uniquely the potentials. I a...

    Ricardo Weder in Inverse Problems of Wave Propagation and Diffraction (1997)

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