Recovery of a time-dependent Hermitian connection and potential appearing in the dynamic Schr\"odinger equation

Alexander Tetlow

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arXiv · 2006.07723

Recovery of a time-dependent Hermitian connection and potential appearing in the dynamic Schr\"odinger equation

Alexander Tetlow

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Abstract

We consider, on a trivial vector bundle over a Riemannian manifold with boundary, the inverse problem of uniquely recovering time- and space-dependent coefficients of the dynamic, vector-valued Schr\"odinger equation from the knowledge of the Dirichlet-to-Neumann map. We show that the D-to-N map uniquely determines both the connection form and the potential appearing in the Schr\"odinger equation, under the assumption that the manifold is either a) two-dimensional and simple, or b) of higher dimension with strictly convex boundary and admits a smooth, strictly convex function.

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Alexander Tetlow. 2020-06-13. Recovery of a time-dependent Hermitian connection and potential appearing in the dynamic Schr\"odinger equation. https://arxiv.org/abs/2006.07723

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