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Semiclassical resolvent estimates for two and three-body Schrödinger operators. (English) Zbl 0711.35095
The purpose of this work is to establish uniform resolvent estimates for semiclassical three-body Schrödinger operators under a nontrapping condition for the classical flow of all subsystems. The author also proves resolvent estimates for two-body Schrödinger operators with positive potentials when the energy level and the Planck constant tend both to zero. This extends previous results by D. Robert and H. Tamura [Ann. Inst. Henri Poincaré, Phys. Theor. 46, 415-442 (1987; Zbl 0648.35066)] and X. P. Wang [Asymptotiques semiclassiques pour les opérateur de Schrödinger et de Dirac, Thèse d’État (1986); see also Ann. Inst. Henri Poincaré, Phys. Theor. 43, 269-319 (1985; Zbl 0614.35074)].
Reviewer: B.Helffer

MSC:
35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
81U10 \(n\)-body potential quantum scattering theory
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