The Dirichlet-to-Neumann map in a disk with a one-step radial potential. An analytical and numerical study

We consider the Schr"odinger operator with a potential q on a disk and the map that associates to q the corresponding Dirichlet to Neumann (DtN) map. We give some numerical and analytical results on the range of this map and its stability, for the particular class of one-step radial potentials.