  For decreasing sequences $\{t_{n}\}_{n=1}^{\infty}$ converging to zero, we
obtain the almost everywhere convergence results for sequences of
Schr\"{o}dinger means $e^{it_{n}\Delta}f$, where $f \in H^{s}(\mathbb{R}^{N}),
N\geq 2$. The convergence results are sharp up to the endpoints, and the method
can also be applied to get the convergence results for the fractional
Schr\"{o}dinger means and nonelliptic Schr\"{o}dinger means.
