  Let $\mathcal{L}$ be the Schr\"odinger operator with potential $V$, that is,
$\mathcal L=-\Delta+V$, where it is assumed that $V$ satisfies a reverse
H\"older inequality. We consider weighted Morrey-Campanato spaces
$BMO_{\mathcal L,w}^\alpha (\mathbb R^d)$ and $BLO_{L,w}^\alpha (\mathbb R^d)$
in the Schr\"odinger setting. We prove that the variation operator $V_\sigma
(\{T_t\}_{t>0})$, $\sigma>2$, and the oscillation operator $O(\{T_t\}_{t>0},
\{t_j\}_{j\in \mathbb Z})$, where $t_j<t_{j+1}$, $j\in \mathbb Z$,
$\lim_{j\rightarrow +\infty}t_j=+\infty$ and $\lim_{j\rightarrow -\infty}
t_j=0$, being $T_t=t^k\partial_t^k e^{-t\mathcal L}$, $t>0$, with $k\in \mathbb
N$, are bounded operators from $BMO_{\mathcal L,w}^\alpha (\mathbb R^d)$ into
$BLO_{\mathcal L,w}^\alpha (\mathbb R^d)$. We also establish the same property
for the maximal operators defined by $\{t^k\partial_t^k e^{-t\mathcal
L}\}_{t>0}$, $k\in \mathbb N$.
