  The goal of this note is to establish non-tangential convergence results for
Schr\"{o}dinger operators along restricted curves. We consider the relationship
between the dimension of this kind of approach region and the regularity for
the initial data which implies convergence. As a consequence, we obtain a upper
bound for $p$ such that the Schr\"{o}dinger maximal function is bounded from
$H^{s}(\mathbb{R}^{n})$ to $L^{p}(\mathbb{R}^{n})$ for any $s >
\frac{n}{2(n+1)}$.
