  We study the Schr\"odinger-Poisson (SP) method in the context of cosmological
large-scale structure formation in an expanding background. In the limit $\hbar
\to 0$, the SP technique can be viewed as an effective method to sample the
phase space distribution of cold dark matter that remains valid on non-linear
scales. We present results for the 2D and 3D matter correlation function and
power spectrum at length scales corresponding to the baryon acoustic
oscillation (BAO) peak. We discuss systematic effects of the SP method applied
to cold dark matter and explore how they depend on the simulation parameters.
In particular, we identify a combination of simulation parameters that controls
the scale-independent loss of power observed at low redshifts, and discuss the
scale relevant to this effect.
