On the scaling properties of excited stationary states of the Schrödinger-Poisson model

• We provide heuristic laws for excited Schrödinger-Poisson eigenstates. • Based on the heuristic laws, we fit the model to experimental rotation curves. • In the fitting procedure, heuristic laws guide a preselection of the parameter space. • The preselection makes parameter space exploration computationally feasible. In this work, numerical computations of excited spherically symmetric stationary states of the Schrödinger-Poisson system are performed. Novel heuristic relationships are established, that accurately describe their fundamental features as functions of the excitation index. The derived scaling laws play a fundamental role in model fitting procedures, significantly optimizing the parameter space exploration and thereby enhancing computational efficiency. The practical applicability of this methodology in astrophysical and cosmological contexts is demonstrated by successfully fitting the model to dark matter rotation curves from the SPARC database.