Cosmological fluid dynamics in the Schr\"odinger formalism

Understand

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.