Determination of separable perturbations of an unbounded potential in the two-dimensional Schr\"odinger equation

Summary · qwen2.5:32b

The study establishes uniqueness and stability for determining separable perturbations of an unbounded potential in a two-dimensional Schrödinger equation using the Dirichlet-to-Neumann map, which is crucial for inverse problems in quantum mechanics. The proof leverages a particular Carleman inequality to achieve these results.

Suggested post angle

Discussing the Schrödinger equation and its perturbations in two-dimensional space with a separated product structure.

Excerpt

arXiv:2606.18407v3 Announce Type: replace Abstract: We establish uniqueness and stability results for a class of perturbations of an unbounded potential in the two-dimensional Schr\"odinger equation, from the corresponding Dirichlet-to-Neumann map. We assume that the difference between the potentials has a separated product structure. Our proof relies on a specific Carleman inequality.