Conditional Stability of Coefficients Inverse Problem for Strongly Coupled Schr\"odinger Equations

TL;DR

This paper establishes new stability results for inverse problems involving strongly coupled Schrödinger equations, enabling the recovery of stationary potentials from boundary or internal measurements using novel Carleman estimates.

Contribution

It introduces a new Carleman estimate for strongly coupled Schrödinger equations and derives two stability results for inverse potential problems.

Findings

Derived two stability results for inverse problems

Established a new Carleman estimate for coupled Schrödinger equations

Demonstrated potential recovery from boundary and internal data

Abstract

This paper concerns inverse problems for strongly coupled Schr\"odinger equations. The purpose of this inverse problem is to retrieve a stationary potential in the strongly coupled Schr\"odinger equations from either boundary or internal measurements. Two stability results are derived from a new Carleman estimate for the strongly coupled Schr\"odinger equations.