  We propose an approach to analytically solve the quantum dynamics of bosonic
systems. The method is based on reconstructing the quantum state of the system
from the moments of its annihilation operators, dynamics of which is solved in
the Heisenberg picture. The proposed method is general in the sense that it
does not assume anything on the initial conditions of the system such as
separability, or the structure of the system such as linearity. It is an
alternative to the standard master equation approaches, which are analytically
demanding especially for large multipartite quantum systems. To demonstrate the
proposed technique, we apply it to a system consisting of two coupled damped
quantum harmonic oscillators.
