  In this paper we study the boundedness in weighted variable Lebesgue spaces
of operators associated with the semigroup generated by the time-independent
Schr\"odinger operator $\mathcal{L}=-\Delta+V$ in $\mathbb{R}^d$, where $d>2$
and the non-negative potential $V$ belongs to the reverse H\"older class $RH_q$
with $q>d/2$. Each of the operators that we are going to deal with are singular
integrals given by a kernel $K(x,y)$, which satisfies certain size and
smoothness conditions in relation to a critical radius function $\rho$ which
comes appears naturally in the harmonic analysis related to Schr\"odinger
operator $\mathcal{L}$.
