Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Semiclassical singularities propagation property for Schrödinger equations
Shu Nakamura
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2009 Volume 61 Issue 1 Pages 177-211

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Abstract
We consider Schrödinger equations with variable coefficients, which are long-range type perturbations of the flat Laplacian on Rn. We characterize the wave front set of solutions to Schrödinger equations in terms of the initial state. Then it is shown that the singularities propagates along the classical flow, and results are formulated in a semiclassical setting. Methods analogous to the long-range scattering theory, in particular a modified free propagator, are employed.
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© 2009 The Mathematical Society of Japan
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