  The dynamics of a quantum plasma can be described self-consistently by the
nonlinear Schroedinger-Poisson system. Here, we consider a multistream model
representing a statistical mixture of N pure states, each described by a
wavefunction. The one-stream and two-stream cases are investigated. We derive
the dispersion relation for the two-stream instability and show that a new,
purely quantum, branch appears. Numerical simulations of the complete
Schroedinger-Poisson system confirm the linear analysis, and provide further
results in the strongly nonlinear regime. The stationary states of the
Schroedinger-Poisson system are also investigated. These can be viewed as the
quantum mechanical counterpart of the classical Bernstein-Greene-Kruskal modes,
and are described by a set of coupled nonlinear differential equations for the
electrostatic potential and the stream amplitudes.
