Semiclassical Singularity Propagation Property for Schrödinger Equations
Shu Nakamura
Abstract
We consider Schrödinger equations with variable coefficients, and it is supposed to be a long-range type perturbation 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 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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