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

## TL;DR

This paper investigates the Dirichlet-to-Neumann map for a Schrödinger operator with a one-step radial potential in a disk, providing analytical and numerical insights into its range and stability.

## Contribution

It offers new analytical and numerical analysis of the DtN map specifically for one-step radial potentials, enhancing understanding of its properties.

## Key findings

- Characterization of the range of the DtN map
- Analysis of the stability of the map
- Numerical validation of theoretical results

## Abstract

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.