Let $f \in C^2_b(\mathbb{R}^d)$ and $V \in C_b(\mathbb{R}^d)$. Suppose $u : \mathbb{R}_+ \times \mathbb{R}^d \to \mathbb{R}$ satisfies the equation \begin{align*} \partial_t u &= Lu + V(x) u \quad \text{on } \mathbb{R}_+ \times \mathbb{R}^d, \\ u(0, \cdot) &= f \quad \text{on } \mathbb{R}^d. \end{align*} Let $X$ be a solution to $\mathcal{E}_x(\sigma, b)$. Then for all $t > 0$ and $x \in \mathbb{R}^d$, \begin{align*} u(t, x) = \mathbb{E}_x\!\left[f(X_t) \exp\!\left(\int_0^t V(X_s) \, ds\right)\right]. \end{align*}