Anomalous spreading of power-law quantum wave packets

We introduce power-law tail quantum wave packets. We show that they can be seen as eigenfunctions of a Hamiltonian with a physical potential. We prove that the free evolution of these packets presents an asymptotic decay of t he maximum of the wave packets which is anomalous for an interval of the ch aracterizing power-law exponent. We also prove that the number of finite mo ments of the wave packets is a conserved quantity during the evolution of t he wave packet in the free space.