  The problem of the initial conditions for the oscillator model of quantum
dissipative systems is studied. It is argued that, even in the classical case,
the hypothesis that the environment is in thermal equilibrium implies a
statistical correlation between environment oscillators and central system. A
simple form of initial conditions for the quantum problem, taking into account
such a correlation in analogy with the classical ones, is derived on the base
of symmetry considerations. The same symmetries also determine unambiguously
the form of the Lagrangian. As a check of the new form of correlated initial
conditions (and of that of the Lagrangian), the problem of a forced Brownian
particle under the action of arbitrary colored noise is studied: it is shown
that one obtains an average position of a quantum wave packet equal to that of
the corresponding classical Brownian particle. Instead, starting from
uncorrelated initial conditions based on the factorization hypothesis or from a
different form of Lagrangian, non-physical results are obtained. Similar
considerations apply also to the mean square displacement.
