Smoothing effects and dispersion of singularities for the Schrödinger evolution group

We describe smoothing effects and dispersion of singularities for the Schrödinger evolution group in the weighted Sobolev spaces. Under a fairly general assumption on the potential, it is shown that all singularities in the wavefunction vanish instantly whenever the initial state has sufficient decay. We measure the regularity gained by the wavefunction by the decay property of the initial state. No assumptions on the regularity of the initial state are imposed throughout the paper.