Maximal estimates for Schroedinger equation with inverse-square potential

In this paper, we consider the maximal estimates for the solution to an initial value problem of the linear Schroedinger equation with a singular potential. We show a result about the pointwise convergence of solutions to this special variable coefficient Schroedinger equation with initial data $u_0\in H^s({\mathbb{R}}^n)$ for $s>1\mathrm{/}2$ or radial initial data $u_0\in H^s({\mathbb{R}}^n)$ for $s\ge 1\mathrm{/}4$ and the solution does not converge when $s<1\mathrm{/}4$.