Stationary regime for the quantum dynamics of particles in a randomly varying potential

Quantum dynamics of particles in time-dependent random potential field with Gaussian distribution of realisations probabilities in unbounded space is studied. A constant absorption and monoenergetic extended source of particles are introduced into the Schrödinger equation. The moment of switching-on the source is shifted to the infinite past. Assuming that the fluctuations of the random potential are stationary, the existence of stationary limit for the density matrix averaged over potential realisations is proved. It is checked that in the weak interaction approximation, when additionally the absorption length and spatial scale of the source of particles are of the same order as the free run length, the limit mentioned satisfies the usual stationary equation of radiation transport in scattering medium.