H\"older stable determination of a quantum scalar potential in unbounded cylindrical domains
Yavar Kian (CPT), Quang Sang Phan, Eric Soccorsi (CPT)
TL;DR
This paper establishes a H"older stability result for determining a scalar potential in an infinite cylindrical domain from boundary measurements of the Schr"odinger equation, advancing inverse problem theory in unbounded domains.
Contribution
It provides the first H"older stability estimate for the inverse Schr"odinger problem in unbounded cylindrical domains using boundary Neumann data.
Findings
H"older stability proven for potential recovery
Boundary Neumann observation suffices for stability
Method applicable to unbounded cylindrical geometries
Abstract
We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain from one boundary Neumann observation of the solution. We prove H\"older stability by choosing the Dirichlet boundary condition suitably.
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Mathematical Modeling in Engineering · Composite Material Mechanics