  The long time behavior of scattered wave packets $\psi (x,t)$ from a
finite-range potential is investigated, by assuming $\psi (x,t)$ to be
initially located outside the potential. It is then shown that $\psi (x,t)$ can
asymptotically decrease in the various power laws at long time, according to
its initial characteristics at small momentum. As an application, we consider
the square-barrier potential system and demonstrate that $\psi (x,t)$ exhibits
the asymptotic behavior $t^{-3/2}$, while another behavior like $t^{-5/2}$ can
also appear for another $\psi (x,t)$.
