# Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schr\"odinger Operator with only one Observation

## TL;DR

This paper establishes a stability result for simultaneously identifying the diffusion coefficient and potential in a Schrödinger operator within an unbounded strip, using minimal boundary and temporal data.

## Contribution

It provides the first stability estimate for jointly recovering two coefficients of a Schrödinger operator with limited boundary observations.

## Key findings

- Proves stability for coefficient identification with one boundary observation
- Demonstrates the feasibility of coefficient recovery with minimal data
- Extends previous results to unbounded domains

## Abstract

This article is devoted to prove a stability result for two independent coefficients for a Schr\"odinger operator in an unbounded strip. The result is obtained with only one observation on an unbounded subset of the boundary and the data of the solution at a fixed time on the whole domain.