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Lower bounds for shape resonances widths of long range Schrödinger operators. (English) Zbl 1013.35019
The goal of this paper is the study of the localization of resonances for the semiclassical Schrödinger operator near positive energy levels. The shape resonances are the metastable states of a system whose evolution is described by a Hamiltonian, $$H$$, depending upon the Plank constant $$h$$. Here, the author gives general lower bounds of shape resonance widths in the semiclassical limit for Schrödinger operators in the exterior of smooth compact obstacles with Dirichlet or Neumann boundary conditions and with long range dilation analytic potentials.

##### MSC:
 35J10 Schrödinger operator, Schrödinger equation 35B35 Stability in context of PDEs 35B34 Resonance in context of PDEs 47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX) 35J65 Nonlinear boundary value problems for linear elliptic equations
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