Determining the potential and the gradient coupling of two-state quantum systems in an infinite waveguide

Abstract

We consider the inverse coefficient problem of simultaneously determining the space dependent electric potential, the zero-th order coupling term and the first order coupling vector of a two-state Schr\"odinger equation in an infinite cylindrical domain of $\mathbb{R}^n$, $n \ge 2$, from finitely many partial boundary measurements of the solution. We prove that these $n+1$ unknown scalar coefficients can be H\"older stably retrieved by $(n+1)$-times suitably changing the initial condition attached at the system.