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Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections. (English) Zbl 0648.35066
The semi-classical estimates for the resolvent of the Schrödinger operator for Planck’s constant \(h\to 0\) are obtained by the use of the Mourre commutator method. This technical result is used to improve earlier results on the semi-classical asymptotics of the total scattering cross-sections. For related recent results see the author [Jap. J. Math., New Ser. 13, 77-126 (1987)]; D. R. Yafaev [Izv. Akad. Nauk USSR, Ser. Math. 52, No.1, 139-163 (1988)].
Reviewer: G.Nencin

MSC:
35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
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