Gravitational collapse in the Schrödinger-Poisson system

We perform a quantitative comparison between N-body simulations and the Schrödinger-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 $\hbar$ and also test virialization. We discuss the generation of higher order cumulants ofthe particle distribution function which demonstrates that the Schrödinger-Poisson equations should not be perceived as a generalization of the dust model with quantum pressure butrather 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 densityprofile from N-body simulations