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Prolongement méromorphe de la matrice de scattering pour des problèmes à deux corps à longue portée. (Meromorphic extension of the scattering matrix for long range two body problems). (French) Zbl 0711.35097

Summary: We prove the existence of a meromorphic extension of the scattering matrix for long range potentials analytic at infinity. This extension exists as a bounded operator on some Gevrey spaces on \(S^{n-1}\), with critical depending on the rate of decay of the potential at infinity. We use a semi-stationary definition of the scattering operator due to Isozaki-Kitada, using time dependent modifiers. We show that the poles of the scattering matrix coincide with the resonances of the Hamiltonian.

MSC:

35P25 Scattering theory for PDEs
81U05 \(2\)-body potential quantum scattering theory
35J10 Schrödinger operator, Schrödinger equation
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