Finite difference method for an optimal control problem of quantum processes (Q918643)

An optimal control problem for a controlled nonstationary Schrödinger equation is introduced where the performance criterion is a square integral functional with fixed final time. The optimal control problem is an example of the linear regulator type. The Schrödinger equation is approximated by a sequence of difference equations with discrete time and space variables. The performance criterion is approximated by a sum functional. It is proved that the optimal controls of the discrete problems define a minimizing sequence of the original problem. An error estimation is given.