An inverse boundary value problem for Schrödinger operators with vector potentials

Sun, Zi Qi

doi:10.1090/S0002-9947-1993-1179400-1

An inverse boundary value problem for Schrödinger operators with vector potentials
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Trans. Amer. Math. Soc. 338 (1993), 953-969 Request permission

Abstract:

We consider the Schrödinger operator for a magnetic potential $\vec A$ and an electric potential $q$, which are supported in a bounded domain in ${\mathbb {R}^n}$ with $n \geq 3$. We prove that knowledge of the Dirichlet to Neumann map associated to the Schrödinger operator determines the magnetic field $\operatorname {rot}(\vec A)$ and the electric potential $q$ simultaneously, provided $\operatorname {rot}(\vec A)$ is small in the ${L^\infty }$ topology.

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