title: Anomalous spreading of power-Law quantum wave packets
abstract: 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 the maximum of the wave packets which is anomalous for an interval of the characterizing power-law exponent. We also prove that the number of finite moments of the wave packets is a conserved quantity during the evolution of the wave packet in the free space.
authors.affiliation: Istituto Nazionale per la Fisica della Materia, Unita di Palermo and Dipartimento di Energetica ed Applicazioni di Fisica, Universita di Palermo, Viale delle Scienze, I-90128, Palermo, Italia.
authors.initials: F
authors.lastname: Lillo
authors.initials: RN
authors.lastname: Mantegna