  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 nonnegative
potential $V$ 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 variable
exponent function satisfying the globally $\log$-H\"{o}lder continuous
condition. The authors introduce the variable Hardy space
$H_L^{p(\cdot)}(\mathbb{R}^n)$ associated to $L$ and establish its atomic
characterization. The atoms here are closer to the atoms of variable Hardy
space $H^{p(\cdot)}(\mathbb{R}^n)$ in spirit, which further implies that
$H^{p(\cdot)}(\mathbb{R}^n)$ is continuously embedded in
$H_L^{p(\cdot)}(\mathbb{R}^n)$.
