# Infinite propagation speed for the Schrodinger operator

Question related to: On the propagation of singularities in PDE and Hypoellipticity and singular support.

in what sense is to interpret the sentence the schrodinger operator has infinite propagation speed. And what about the fact that if there is a singularity at $t=0$, then at $t=\epsilon$ there isn't anymore?

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Consider the Schrodinger equation with an initial condition supported in a bounded region. At any positive $t$, the wave function is nonzero arbitrarily far away. In that sense, the particle can travel (albeit with small probability) at arbitrarily high speeds.