Transport in the One-Dimensional Schroedinger Equation

Details Transport in the One-Dimensional Schroedinger Equation Transport in the One-Dimensional Schroedinger Equation

2006-06-08

arxiv.org/abs/math/0606172v1

Mathematics

Analysis of PDEs

8 Pages

Scientific paper

we prove a dispersive estimate for the one-dimensional Schroedinger equation, mapping between weighted L^p spaces with stronger time-decay (t^{-3/2} versus t^{-1/2}) than is possible on unweighted spaces. To satisfy this bound, the long-term behavior of solutions must include transport away from the origin. Our primary requirements are that (1+|x|)^3 V be integrable and -\Delta + V not have a resonance at zero energy. If a resonance is present (for example in the free case), similar estimates are valid after projecting away from a rank-one subspace corresponding to the resonance.

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