  We consider the nonlinear fractional problem
  \begin{align*}
  (-\Delta)^{s} u + V(x) u = f(x,u) &\quad \hbox{in $\mathbb{R}^N$}
\end{align*} We show that ground state solutions converge (along a subsequence)
in $L^2_{\mathrm{loc}} (\mathbb{R}^N)$, under suitable conditions on $f$ and
$V$, to a weak solution of the local problem as $s \to 1^-$.
