We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in ${ℝ}^n$. Also, for symmetric second-order ordinary differential operators we show that ${lim\; sup}_{t\to c}{\left(p{q}^{\text{'}}\right)}^{\text{'}}/q^2=\theta <2$ where $c$ is a singular point guarantees separation of $-{\left(p{y}^{\text{'}}\right)}^{\text{'}}+qy$ on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that $-\Delta y+qy$ is separated on its minimal domain if $q$ is superharmonic. For $n=1$ the criterion...