  Often considered in numerical simulations related to the control of quantum
systems, the so-called monotonic schemes have not been so far much studied from
the functional analysis point of view. Yet, these procedures provide an
efficient constructive method for solving a certain class of optimal control
problems. This paper aims both at extending the results already available about
these algorithms in the finite dimensional case (i.e., the time-discretized
case) and at completing those of the continuous case. This paper starts with
some results about the regularity of a functional related to a wide class of
model in quantum chemistry. Those enable us to extend an inequality due to
