  Fuzzy dark matter (FDM) made of ultra-light bosonic particles is a viable
alternative to cold dark matter (CDM) with clearly distinguishable small-scale
features in collapsed structures. On large scales, it behaves gravitationally
like CDM deviating only by a cut-off in the initial power spectrum and can be
studied using N-body methods. In contrast, wave interference effects near the
de Broglie scale result in new phenomena unique to FDM. Interfering modes in
filaments and halos yield a stochastically oscillating granular structure which
condenses into solitonic cores during halo formation. Investigating these
highly non-linear wave phenomena requires the spatially resolved numerical
integration of the Schr\"odinger equation. In previous papers we introduced a
hybrid zoom-in scheme that combines N-body methods to model the large-scale
gravitational potential around and the mass accretion onto pre-selected halos
with simulations of the Schr\"odinger-Poisson equation to capture wave-like
effects inside these halos. In this work, we present a new, substantially
improved reconstruction method for the wave function inside of previously
collapsed structures. We demonstrate its capabilities with a deep zoom-in
simulation of a well-studied sub-$L_\ast$-sized galactic halo from cosmological
intitial conditions. With a particle mass of $m = 2.5\times 10^{-22}\,$eV and
halo mass $M_{\text{vir}}=1.7\times 10^{11}\,M_{\odot}$ in a ($60$h${^{-1}}$
comoving Mpc)${}^{3}$ cosmological box, it reaches an effective resolution of
20 comoving pc. This pushes the values of $m$ and $M$ accessible to simulations
significantly closer to those relevant for studying galaxy evolution in the
allowed range of FDM masses.
