  We propose a Newton algorithm to characterize the Hamiltonian of a quantum
system interacting with a given laser field. The algorithm is based on the
assumption that the evolution operator of the system is perfectly known at a
fixed time. The computational scheme uses the Crank-Nicholson approximation to
explicitly determine the derivatives of the propagator with respect to the
Hamiltonians of the system. In order to globalize this algorithm, we use a
continuation method that improves its convergence properties. This technique is
applied to a two-level quantum system and to a molecular one with a double-well
potential. The numerical tests show that accurate estimates of the unknown
parameters are obtained in some cases. We discuss the numerical limits of the
algorithm in terms of basin of convergence and non uniqueness of the solution.
