Semiclassical Defect Measures and Observability Estimate for Schr\"odinger Operators with Homogeneous Potentials of Order Zero
Abstract
We study the asymptotic behavior as |x| ∞ of Schr\"odinger 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.
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