Breit-Wigner formulas for the scattering phase and the total scattering cross-section in the semi-classical limit |
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| Authors: | C Gérard A Martinez D Robert |
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| Institution: | (1) Centre de Mathématiques, Ecole Polytechnique, F-91128 Palaiseau Cédex, France;(2) Départment de Mathématiques, Université de Paris-Sud, Bât 425, F-91405 Orsay Cédex, France;(3) Départment de Mathématiques, Université de Nantes, 2, chemin de la Houssinière, F-44072 Nantes Cédex 03, France |
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| Abstract: | In this paper we prove results in resonance scattering for the Schrödinger operatorP
v=–h
2 +V, V being a smooth, short range potential onR
n
. More precisely, for energy  near a trapping energy level 0 for the classical system defined by the Hamiltonianp(x, )=
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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| Keywords: | |
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