  We study the large-time asymptotics of the mean-square displacement for the
time-fractional Schrodinger equation in $\mathbb{R}^d$. We define the
time-fractional derivative by the Caputo derivative and we consider the
initial-value problem for the free evolution of wave packets in $\mathbb{R}^d$
governed by the time-fractional Schrodinger equation $ i^\beta
\partial_t^\alpha u = - \Delta u, ~~~~u(t=0) = u_0$, parameterized by two
indices $\alpha, \beta \in (0,1]$. We show distinctly different long-time
evolution of the mean square displacement according to the relation between
$\alpha$ and $\beta$. In particular, asymptotically ballistic motion occurs
only for $\alpha=\beta$.
