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We study the asymptotic behavior as |x| \to \infty of Schr\"odinger operatorswith homogeneous potentials. For this purpose, we use methods fromsemiclassical analysis and investigate semiclassical defect mesures. We provetheir localization in direction which we apply in order to obtain a necessarycondition of observability.

Semiclassical Defect Measures and Observability Estimate for Schr\"odinger Operators with Homogeneous Potentials of Order Zero