  In this paper we propose a systematic method to solve the inverse dynamical
problem for a quantum system governed by the von Neumann equation: to find a
class of Hamiltonians reproducing a prescribed time evolution of a pure or
mixed state of the system. Our approach exploits the equivalence between an
action of the group of evolution operators over the state space and an adjoint
action of the unitary group over Hermitian matrices. The method is illustrated
by two examples involving a pure and a mixed state.
