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Benbernou-Lahmar, Amina

Estimate of the residues of the scattering matrix associated with sharp resonance. I. (Estimation des résidus de la matrice de diffusion associés à des résonances de forme. I.) (French) Zbl 0944.35060

Ann. Inst. Henri Poincaré, Phys. Théor. 71, No. 3, 303-338 (1999).
Summary: The aim of this study is to estimate the residue of the scattering matrix associated with resonances for two-body Schrödinger operators with long range interactions in the semiclassical approach. We assume that there are no caustics out of the classical forbidden area surrounding the well. Then we obtain a semiclassical BKW expansion of the resonating states in a neighhorhood of some vanishing bicharacteristics of the operator. This expansion allows us to find out an estimate of the residue of the kernel of the scattering matrix, which appears to be either of the same order as the width of the resonance, or such depending on the fact that \((\omega,\omega')\) belongs or not to a certain set explicitely described.

Cited in 2 Documents

MSC:

35P25 Scattering theory for PDEs
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81U05 \(2\)-body potential quantum scattering theory
47N50 Applications of operator theory in the physical sciences

Keywords:

two-body Schrödinger operators; long range intcractions; semiclassical approach; semiclassical BKW expansion
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References:

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