Gravitational collapse in the Schr\"odinger-Poisson system
  We perform a quantitative comparison between N-body simulations and the
Schr\"odinger-Poisson system in 1+1 dimensions. In particular, we study halo
formation with different initial conditions. We observe the convergence of
various observables in the Planck constant h-bar and also test virialization.
We discuss the generation of higher order cumulants of the particle
distribution function which demonstrates that the Schr\"odinger-Poisson
equations should not be perceived as a generalization of the dust model with
quantum pressure but rather as one way of sampling the phase space of the
Vlasov-Poisson system -- just as N-body simulations. Finally, we quantitatively
recover the scaling behavior of the halo density profile from N-body
simulations.
