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Time-decay of scattering solutions and classical trajectories. (English) Zbl 0641.35018
Summary: We obtain the best time-decay results for scattering solutions of semiclassical Schrödinger equation with various localizations in the phase space. We show also that the non trapping condition in classical mechanics is in fact equivalent with that in quantum mechanics. The proof of these results is based on the construction of temporal global outgoing or incoming \(h\)-parametrices.

MSC:
35J10 Schrödinger operator, Schrödinger equation
35B40 Asymptotic behavior of solutions to PDEs
35P25 Scattering theory for PDEs
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