Related papers: Determination of matrix potential from scattering …
We give a sharp upper bound on the vanishing order of solutions to Schr\"odinger equation, in the case that the potential is of class $\mathcal{C}^1$ on a smooth compact manifold.
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
Others have solved the Schr\"odinger equation for a one-dimensional model having a square potential barrier in free-space by requiring an incident and a reflected wave in the semi-infinite pre-barrier region, two opposing waves in the…
We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schr\"odinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first…
We consider the Schr\"odinger equation with a multipoint potential of the Bethe-Peierls-Thomas-Fermi type. We show that such a potential in dimension d=2 or d=3 is uniquely determined by its scattering amplitude at a fixed positive energy.…
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…
Using a parameterisation of general self-adjoint boundary conditions in terms of Lagrange planes we propose a scheme for factorising the matrix Schroedinger operator and hence construct a Darboux transformation an interesting feature of…
This is a survey of the basic results on the behavior of the number of the eigenvalues of a Schr\"odinger operator, lying below its essential spectrum. We discuss both fast decaying potentials, for which this behavior is semiclassical, and…
We demonstrate a quantitative version of the usual properties related to unique continuation from an interior datum for the Schr\"odinger equation with bounded or unbounded potential. The inequalities we establish have constants that…
Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let $V$ denote an electric potential driven by a voltage drop between the conducting surfaces of the wire. We consider the operator ${\mathcal…
Probability of reflection $R(E)$ off a finite attractive scattering potential at zero or low energies is ordinarily supposed to be 1. However, a fully attractive potential presents a paradoxical result that $R(0)=0$ or $R(0)<1$, when an…
We prove that radial, monotonic, superexponentially decaying potentials in R^n, n greater than or equal to 1 odd, are determined by the resonances of the associated semiclassical Schrodinger operator among all superexponentially decaying…
Linear theory for phonon scattering by discrete breathers in the discrete nonlinear Schroedinger equation using the transfer matrix approach is presented. Transmission and reflection coefficients are obtained as a function of the wave…
We prove upper bounds on the number of resonances and eigenvalues of Schr\"odinger operators $-\Delta+V$ with complex-valued potentials, where $d\geq 3$ is odd. The novel feature of our upper bounds is that they are \emph{effective}, in the…
We study the microlocal properties of the scattering matrix associated to the semiclassical Schr\"odinger operator $P=h^2\Delta_X+V$ on a Riemannian manifold with an infinite cylindrical end. The scattering matrix at $E=1$ is a linear…
In this paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…
We consider, for $h, E > 0$, resolvent estimates for the semiclassical Schr\"odinger operator $-h^2 \Delta + V - E$. Near infinity, the potential takes the form $V = V_L+ V_S$, where $V_L$ is a long range potential which is Lipschitz with…
This paper investigates the inverse scattering problem for the magnetic Schr\"odinger equation. We first establish the well-posedness of the direct problem through a variational approach under physically meaningful assumptions on the…
We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in…
We prove Buslaev-Faddeev trace identities for the matrix Schr\"odinger operator on the half line, with general boundary conditions at the origin, and with selfadjoint matrix potentials.