We present a wave generalization of the classic Schwarzschild method for
constructing self-consistent halos — such a halo consists of a suitable
superposition of waves instead of particle orbits, chosen to yield a desired
mean density profile. As an illustration, the method is applied to spherically
symmetric halos. We derive an analytic relation between the particle
distribution function and the wave superposition amplitudes, and show how it
simplifies in the high energy (WKB) limit. We verify the stability of such
constructed halos by numerically evolving the Schr\”odinger-Poisson system. The
algorithm provides an efficient and accurate way to simulate the time-dependent
halo substructures from wave interference. We use this method to construct
halos with a variety of density profiles, all of which have a core from the
ground-state wave function, though the core-halo relation need not be the
standard one.
