We show in this paper the conditionthat strongly elliptic differential operators with singular lower order coefficients belonging to a class of measurable functions which includes the Schecter potential class $M_{\sigma ,r,q}$ generate analytic semigroups. particularly, the class includes $L^p({\text{boldmath }R}^n)$. As an application, we obtain a result for $L^p({\text{boldmath }R}^n)$ lower order coefficients, where $p$ can be taken as some critical values.