Semiclassical Defect Measures and Observability Estimate for Schrödinger Operators with Homogeneous Potentials of Order Zero

Abstract

We study the asymptotic behavior as |x| \to \infty of Schrödinger operators with homogeneous potentials. For this purpose, we use methods from semiclassical analysis and investigate semiclassical defect mesures. We prove their localization in direction which we apply in order to obtain a necessary condition of observability.

24 pages. We improved the statement of the main theorem. We also fixed some mistakes