One-dimensional perturbations of operators

Perturbations of One - Dimensional Schr

Rank one perturbations of self-adjoint operators

The Width of Resonances for Slowly Varying Perturbations of One-dimensional Periodic Schrödinger Operators

In this talk, we report on results about the width of the resonances for a slowly varying perturbation of a periodic operator. The study takes place in dimension one. The perturbation is assumed to be analytic and local in the sense that it tends to a constant at +∞ and at −∞; these constants may differ. Modulo an assumption on the relative position of the range of the local perturbation with r...

Spectral Deformations of One-dimensional Schrödinger Operators

We provide a complete spectral characterization of a new method of constructing isospectral (in fact, unitary) deformations of general Schrödinger operators H = − d2 dx2 + V in L2(R). Our technique is connected to Dirichlet data, that is, the spectrum of the operator HD on L2((−∞, x0))⊕L2((x0 ,∞)) with a Dirichlet boundary condition at x0. The transformation moves a single eigenvalue of HD and ...

On the Numerical Solution of One Dimensional Schrodinger Equation with Boundary Conditions Involving Fractional Differential Operators

In this paper we study of collocation method with Radial Basis Function to solve one dimensional time dependent Schrodinger equation in an unbounded domain. To this end, we introduce artificial boundaries and reduce the original problem to an initial boundary value problem in a bounded domain with transparent boundary conditions that involves half order fractional derivative in t. Then in three...