On the problem of recovering the $\psi$-function in nonrelativistic quantum mechanics

It is shown that the $\psi$-function for an ensemble of particles prepared in one and the same state can be recovered by placing these particles in appropriate potential fields and measuring the distribution of the coordinates and the momenta at different times. It is sufficient to make the measurements for $t\in[t_0, t_0 +\Delta t]$ with arbitrarily short $\Delta t$.