Abstract
We study the semiclassical Schrödinger operator, − h 2 Δ + V( x), h ϵ ]0, 1], and establish various results on the time-decay of scattering solutions and the semiclassical bounds for the powers of the resolvent. For short range potentials, the time-decay results obtained in this paper are the best possible and this enables us to conclude the equivalence between the non-trapping condition in classical mechanics and the uniform time-decay of wave functions in quantum mechanics.
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