In this paper,  the parabolic Schrodinger operator  $\mathcal{P}=\partial_t-\Delta +V(x)$  on $\mathbb{R}^{n+1}$ is considered, where  $n\geq 3,$  nonnegative potential $V$  belongs to the reverse H\"older class  $RH_q$  with  $q\geq n/2.$  The  $L^p$  boundedness of operators $V^{\alpha}\mathcal{P}^{-\beta},$ $ V^\alpha \nabla \mathcal{P}^{-\beta}$  and their  adjoint operators are  established.