The Dirichlet-to-Neumann Map in a Disk with a One-Step Radial Potential: An Analytical and Numerical Study

Abstract

Herein, we considered the Schrödinger operator with a potential q on a disk and the map that associates to q the corresponding Dirichlet-to-Neumann (DtN) map. We provide some numerical and analytical results on the range of this map and its stability for the particular class of one-step radial potentials.