Lévy–Schrödinger wave packets

We analyze the time–dependent solutions of the pseudo–differential Lévy–Schrödinger wave equation in the free (force-less) case, and we compare them with the associated Lévy processes. We first list the principal laws used to describe the time evolutions of both Lévy process densities and Lévy–Schrödinger wave packets. To have self–adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible Lévy noises with laws symmetric under change of sign of the independent variable. We then show a few examples of the characteristic behavior of the Lévy–Schrödinger wave packets, and in particular of the bi-modality arising in their evolutions: a feature at variance with the typical diffusive unimodality of the Lévy process densities.