  We simulate the formation and evolution of ultralight bosonic dark matter
halos from cosmological initial conditions. Using zoom-in techniques we are
able to resolve the detailed interior structure of the halos. We observe the
formation of solitonic cores and confirm the core-halo mass relation previously
found by Schive et al. The cores exhibit strong quasi-normal oscillations that
remain largely undamped on evolutionary timescales. On the other hand, no
conclusive growth of the core mass by condensation or relaxation can be
detected. In the incoherent halo surrounding the cores, the scalar field
density profiles and velocity distributions show no significant deviation from
collisionless N-body simulations on scales larger than the coherence length.
Our results are consistent with the core properties being determined mainly by
the coherence length at the time of virialization, whereas the
Schr\"odinger-Vlasov correspondence explains the halo properties when averaged
on scales greater than the coherence length.
