Gravitational atoms: general framework for the construction of
  multistate axially symmetric solutions of the Schr\"odinger-Poisson system
  We present a general strategy to solve the stationary Schr\"odinger-Poisson
(SP) system of equations for multistates with axial symmetry. The approach
allows us to obtain the well known single and multistate solutions with
spherical symmetry, Newtonian multistate $\ell-$boson stars and axially
symmetric multistate configurations. For each case we construct particular
examples that illustrate the method, whose stability properties are studied by
numerically solving the time-dependent SP system. Among the stable
configurations there are the mixed-two-state configurations including spherical
and dipolar components, which might have an important value as potential
anisotropic dark matter halos in the context of ultralight bosonic dark matter
scenarios. This is the reason why we also present a possible process of
formation of these mixed-two-state configurations that could open the door to
the exploration of more general multistate structure formation scenarios.
