  We consider the problem of determining the unknown parameters of the
Hamiltonian of a network of spin 1/2 particles. In particular, we study
experiments in which the system is driven by an externally applied
electro-magnetic field and the expectation value of the total magnetization is
measured. Under appropriate assumptions, we prove that, if it is possible to
prepare the system in a known initial state, the above experiment allows to
identify the parameters of the Hamiltonian. In the case where the initial state
is itself an unknown parameter, we characterize all the pairs
Hamiltonian-Initial State which give the same value of the magnetization for
every form of the driving electro-magnetic field. The analysis is motivated by
recent results on the isospectrality of Hamiltonians describing Magnetic
Molecules.
