  In this paper, the compressible quantum model with the given mass source and
the external force of general form in three-dimensional whole space is
considered. Based on the weighted $L^2$ method and $L^\infty$ estimates, the
existence and uniqueness of stationary solutions can be obtained by the
contraction mapping principle. By using a general energy method, the nonlinear
stability of stationary solutions is studied, and the time decay rates of the
solutions are established when the initial perturbation belongs to
$\dot{H}^{-s}$ with $0 \leq s < \frac{3}{2}$.
