Semiclassical Singularity Propagation Property for Schrödinger Equations

Details Semiclassical Singularity Propagation Property for Schrödinger Equations Semiclassical Singularity Propagation Property for Schrödinger Equations

2006-05-30

arxiv.org/abs/math/0605742v2

Mathematics

Analysis of PDEs

29 pages

Scientific paper

We consider Schr\"odinger equations with variable coefficients, and it is supposed to be a long-range type perturbation of the flat Laplacian on $R^n$. We characterize the wave front set of solutions to Schr\"odinger equations in terms of the initial state. Then it is shown that the singularity propagates following the classical flow, and it is formulated in a semiclassical settings. Methods analogous to the long-range scattering theory, in particular a modified free propagator, are employed.

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