Applied Mathematical Sciences
Volume 1 / 1971 to Volume 204 / 2020
手机体育投注平台 Book Series
Volume 1 / 1971 to Volume 204 / 2020
Book
Chapter
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...
Chapter
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...
Chapter
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...
手机体育投注平台 Chapter
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...
手机体育投注平台 Chapter
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...
手机体育投注平台 Chapter
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...
Article
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 ′
手机体育投注平台 Article
We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator $${...
Article
We analyze spin-0 relativistic scattering of charged particles propagating in the exterior, \({\Lambda \subset \mathbb{R}^3}\) ...
手机体育投注平台 Article
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...
Article
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...
手机体育投注平台 Article
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...
Article
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...
Chapter and Conference Paper
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...
Chapter and Conference Paper
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...
Article
In this paper we study the following nonlinear Schrödinger equation on the line,
Article
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...
Chapter and Conference Paper
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...