Lower bounds for shape resonances widths of long range Schrödinger operators. (English) Zbl 1013.35019

Burq, Nicolas

Am. J. Math. 124, No. 4, 677-735 (2002).

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.

Reviewer: Messoud Efendiev (Berlin)

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
35J65	Nonlinear boundary value problems for linear elliptic equations

Keywords:

Schrödinger operator; metastable states; Hamiltonian semiclassical limit