  Assuming an effective quadratic Hamiltonian, we derive an approximate, linear
stochastic equation of motion for the density-fluctuations in liquids, composed
of overdamped Brownian particles. From this approach, time dependent two point
correlation functions (such as the intermediate scattering function) are
derived. We show that this correlation function is exact at short times, for
any interaction and, in particular, for arbitrary external potentials so that
it applies to confined systems. Furthermore, we discuss the relation of this
approach to previous ones, such as dynamical density functional theory as well
as the formally exact treatment. This approach, inspired by the well known
Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of
motion, may be seen as its microscopic version, containing information about
the details on the particle level.
