  Exact solutions of the Caldeira-Leggett Master equation for the reduced
density matrix for a free particle and for a harmonic oscillator system coupled
to a heat bath of oscillators are obtained for arbitrary initial conditions.
The solutions prove that the Fourier transform of the density matrix at time t
with respect to (x + x')/2, where x and x' are the initial and final
coordinates, factorizes exactly into a part depending linearly on the initial
density matrix and a part independent of it. The theorem yields the exact
initial state dependence of the density operator at time t and its eventual
diagonalization in the energy basis.
