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Breit-Wigner formula for the scattering phase in the Stark effect. (English) Zbl 0705.35093

A Schrödinger operator in \(n\) dimensions with homogeneous electric field is considered. The leading asymptotics of the derivative of the scattering phase is obtained in the weak field limit near a simple resonance. This is done by a study of the asymptotics of the spectral function; this involves estimates of the boundary values of the resolvent on the real axis. As an application the Breit-Wigner formula which relates the width of a resonance to the time delay is proven; furthermore it is indicated how information about the asymptotic behaviour of the cross section can be obtained.
Reviewer: J.Asch

MSC:

35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
81U20 \(S\)-matrix theory, etc. in quantum theory
35B20 Perturbations in context of PDEs
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