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

TL;DR

This paper develops a method to stably determine multiple unknown coefficients in a two-state Schrödinger equation within an infinite waveguide using finitely many boundary measurements, advancing inverse problem techniques.

Contribution

It introduces a novel approach to simultaneously recover electric potential and coupling terms in a multi-coefficient Schrödinger system from boundary data.

Findings

Successfully reconstructs coefficients with Hölder stability.

Requires only finitely many boundary measurements.

Employs multiple initial conditions for coefficient identification.

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.