We investigate the dynamics of a cosmological dark matter fluid in the Schrödinger 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 multiparticle 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 Schrödinger formulation as a genuine alternative to standard methods in certain contexts, and a novel way to model multiple fluids.