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arXiv · 2503.13863

Recovering All Coefficients in the Schr\"{o}dinger Equation With Finite Sets of Boundary Measurements

Shitao Liu·Antonio Pierrottet
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Abstract

We consider an inverse problem of recovering all spatial dependent coefficients in the time dependent Schr\"odinger equation defined on an open bounded domain in $\mathbb{R}^n$, $n\geq 2$, with smooth enough boundary. We show that by appropriately selecting a finite number of initial conditions and a fixed Dirichlet boundary condition, we may recover all the coefficients in a Lipschitz stable fashion from the corresponding finitely many boundary measurements made on a portion of the boundary. The proof is based on a direct approach, which was introduced in \cite{HIY2020}, to derive the stability estimate directly from the Carleman estimates without any cut-off procedure or compactness-uniqueness argument.

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Shitao Liu, Antonio Pierrottet. 2025-03-18. Recovering All Coefficients in the Schr\"{o}dinger Equation With Finite Sets of Boundary Measurements. https://arxiv.org/abs/2503.13863

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