Abstract
In this paper we prove results in resonance scattering for the Schrödinger operatorP v=−h 2Δ+V, V being a smooth, short range potential onR n. More precisely, for energy λ near a trapping energy level λ0 for the classical system defined by the Hamiltonianp(x,ζ)=ζ 2+V(x), we prove that the scattering phase and the scattering cross sections associated to (P v, P0) have the Breit-Wigner form (“Lorentzian line shape”) in the limith→0.
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Gérard, C., Martinez, A. & Robert, D. Breit-Wigner formulas for the scattering phase and the total scattering cross-section in the semi-classical limit. Commun.Math. Phys. 121, 323–336 (1989). https://doi.org/10.1007/BF01217809
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DOI: https://doi.org/10.1007/BF01217809