  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.
