On unique continuation of solutions of Schr\"odinger equations

We study uniqueness properties of solutions of Schr"odinger equations. The aim is to obtain sufficient conditions on the decay behavior of the difference of two solution $u_1-u_2$ of the equation at two different times $t_0=0$ and $t_1=1$ which guarantee the uniqueness of the solution, i.e. that $u_1\equiv u_2$.