  We prove some local smoothing estimates for the Schr\"{o}dinger initial value
problem with data in $L^2(\mathbb{R}^d)$, $d \geq 2$ and a general class of
potentials. In the repulsive setting we have to assume just a power like decay
$(1+|x|)^{-\gamma}$ for some $\gamma>0$. Also attractive perturbations are
considered. The estimates hold for all time and as a consequence a weak
dispersion of the solution is obtained. The proofs are based on similar
estimates for the corresponding stationary Helmholtz equation and Kato H-smooth
theory.
