Cosmological fluid dynamics in the Schr\"odinger formalism
  We investigate the dynamics of a cosmological dark matter fluid in the
Schr\"odinger formulation, seeking to evaluate the approach as a potential tool
for theorists. We find simple wave-mechanical solutions of the equations for
the cosmological homogeneous background evolution of the dark matter field, and
use them to obtain a piecewise analytic solution for the evolution of a
compensated spherical overdensity. We analyse this solution from a `quantum
mechanical' viewpoint, and establish the correct boundary conditions satisfied
by the wavefunction. Using techniques from multi-particle quantum mechanics, we
establish the equations governing the evolution of multiple fluids and then
solve them numerically in such a system. Our results establish the viability of
the Schr\"odinger formulation as a genuine alternative to standard methods in
certain contexts, and a novel way to model multiple fluids.
