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Breit-Wigner formulas for the scattering phase and the total scattering cross-section in the semi-classical limit. (English) Zbl 0704.35114
Authors’ summary: In this paper we prove results in resonance scattering for the Schrödinger operator \(P_ V=-h^ 2\Delta +V\), V being a smooth, short range potential on \({\mathbb{R}}^ n\). More precisely, for energy \(\lambda\) near a trapping energy level \(\lambda_ 0\) for the classical system defined by the Hamiltonian \(p(x,\xi)=\xi^ 2+V(x)\), we prove that the scattering phase and the scattering cross sections associated to \((P_ V,P_ 0)\) have the Breit-Wigner form (“Lorentzian line shape”) in the limit \(h\to 0\).
Reviewer: X.-P.Wang

MSC:
35P25 Scattering theory for PDEs
35Q40 PDEs in connection with quantum mechanics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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