Abstract

We consider the inverse problem of determining simultaneously two unknown electric potential coefficients for a system of two general strongly coupled Schrödinger equations, with magnetic potential terms, and with Neumann boundary conditions, from single Dirichlet measurements on a portion Γ₁ of the boundary. Under suitable geometrical assumptions on the complementary unobserved portion Γ₀ of the boundary, we show that one can uniquely determine the two unknown potential coefficients in one shot, from respective Dirichlet boundary measurements on Γ₁ over an arbitrarily short time interval. The proof is based on a recent Carleman estimate in [Lasiecka, Triggiani and Zhang, J. Inv. Ill-Posed Problems 12: 43–123, 2004] for single Schrödinger equations. It also takes advantage of a convenient route “post-Carleman estimates” suggested by [Isakov, Inverse Problems for Partial Differential Equations, Springer, 2006, Theorem 8.2.2, p. 231].