Breit-Wigner formula for the scattering phase in the Stark effect (Q917799)

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.