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Let $L:=-\Delta+V$ be the Schr\"{o}dinger operator on $\mathbb{R}^n$ with$n\geq 3$, where $V$ is a non-negative potential which belongs to certainreverse H\"{o}lder class $RH_q(\mathbb{R}^n)$ with $q\in (n/2,\,\infty)$. Inthis article, the authors obtain the quantitative weighted boundedness ofLittlewood--Paley functions $g_L$, $S_L$ and $g_{L,\,\lambda}^\ast$, associatedto $L$, on weighted Lebesgue spaces $L^p(w)$, where $w$ belongs to the class ofMuckenhoupt $A_p$ weights adapted to $L$.

Quantitative Boundedness of Littlewood--Paley Functions on Weighted Lebesgue Spaces in the Schr\"{o}dinger Setting