  In recent times it has been paid attention to the fact that (linear) wave
equations admit of "soliton-like" solutions, known as Localized Waves or
Non-diffracting Waves, which propagate without distortion in one direction.
Such Localized Solutions (existing also for K-G and Dirac equations) are a
priori suitable, more than Gaussian's, for describing elementary particle
motion. In this paper we show that, mutatis mutandis, Localized Solutions exist
even for the ordinary Schroedinger equation, within standard Quantum Mechanics;
and we obtain both approximate and exact solutions, setting forth particular
examples for them. In the ideal case such solutions bear infinite energy, as
well as plane or spherical waves: we also demonstrate, therefore, how to obtain
finite-energy solutions. At last, we briefly consider solutions for a particle
moving in the presence of a potential. Some physical comments are added.
