We present the construction of ground state equilibrium configurations of the
Schr\”odinger-Poisson (SP) system in the Madelung frame and evolve such
configuration using finite volume methods. We compare the behavior of these
configurations when evolved within the SP and Madelung frames, in terms of
conservation of mass and energy. We also discuss the issues of the equations in
the Madelung frame and others inherent to the numerical methods used to solve
them.
