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We present the construction of ground state equilibrium configurations of the Schrödinger–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.