  The solution of the Schrodinger equation with a linear potential is
considered. We use algebraic methods to obtain the explicit form of the
solution for the explicitly time dependent Hamiltonian and discuss the general
conditions which allow us to get solutions in terms of the Airy functions,
yelding non spreading wave packets. We analyze the relevant physical meaning of
these solutions and give examples of their applications. We discuss the analogy
between Airy and Gauss-Weirestrass transform.
