Stable determination of coefficients in the dynamical Schr\"odinger equation in a magnetic field

TL;DR

This paper proves that the electric potential and magnetic field in a Schrödinger equation on a Riemannian manifold can be uniquely and stably determined from boundary measurements, advancing inverse problem theory.

Contribution

It establishes unique identifiability and Hölder stability for the inverse problem of recovering magnetic and electric potentials from boundary data on Riemannian manifolds.

Findings

Unique determination of magnetic field and electric potential

Hölder stability estimates established

Boundary measurements suffice for reconstruction

Abstract

In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential or the magnetic field in a Schr\"odinger equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the magnetic Schr\"odinger equation. We prove that the knowledge of the Dirichlet-to-Neumann map for the Schr\"odinger equation uniquely determines the magnetic field and the electric potential and we establish H\"older-type stability.