Asymptotic behavior of scattering amplitudes in semi-classical and low energy limits

Robert, Didier; Tamura, H.

Annales de l'Institut Fourier, Tome 39 (1989) no. 1, pp. 155-192.

Nous étudions l’asymptotique semi-classique $(h\to 0)$ de l’amplitude de diffusion pour l’opérateur de Schrödinger $-(1/2)h^2\Delta +V$. Nous obtenons une formule asymptotique pour des niveaux d’énergie sans trajectoire captée. De plus la méthode s’applique à l’étude de l’amplitude de diffusion à basse énergie, pour une classe de potentiels répulsifs décroissants assez lentement (non nécessairement à symétrie sphérique).

We study the semi-classical asymptotic behavior as $(h\to 0)$ of scattering amplitudes for Schrödinger operators $-(1/2)h^2\Delta +V$. The asymptotic formula is obtained for energies fixed in a non-trapping energy range and also is applied to study the low energy behavior of scattering amplitudes for a certain class of slowly decreasing repulsive potentials without spherical symmetry.

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