The Hamiltonian operator associated with some quantum stochastic evolutions

We consider the Hamiltonian operator associated to the quantum stochastic differential equation introduced by Hudson and Parthasarathy to describe a quantum mechanical evolution in presence of a ``quantum noise''. We characterize such Hamiltonian in the case of arbitrary multiplicity and bounded coefficients: we find an essentially self-adjoint restriction of the operator and, in particular, we provide an explicit construction of a dense set of vectors belonging to its domain.