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In this article, the authors consider the Schr\"{o}dinger type operator$L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$, where the matrix$A$ is symmetric and satisfies uniformly elliptic condition and the nonnegativepotential $V$ belongs to the reverse H\"{o}lder class $RH_q(\mathbb{R}^n)$ with$q\in(n/2,\,\infty)$. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$ be a variableexponent function satisfying the globally $\log$-H\"{o}lder continuouscondition. The authors introduce the variable Hardy space$H_L^{p(\cdot)}(\mathbb{R}^n)$ associated to $L$ and establish its atomiccharacterization. The atoms here are closer to the atoms of variable Hardyspace $H^{p(\cdot)}(\mathbb{R}^n)$ in spirit, which further implies that$H^{p(\cdot)}(\mathbb{R}^n)$ is continuously embedded in$H_L^{p(\cdot)}(\mathbb{R}^n)$.

Atomic Characterizations of Hardy Spaces Associated to Schr\"{o}dinger Type Operators