  We present a solution of the Schr\"odinger-Poisson system based on the WKB
ansatz for the wave function. In this way we obtain a description of a
gravitationally bound clump of axion dark matter by a superposition of energy
eigenstates with random phases. It can be applied to any self-consistent pair
of radial density distribution and phase space density $f(E)$ related by
Eddington's formula. We adopt this as a model for axion miniclusters in our
galaxy and use it to study the mass loss due to a star encounter by using
standard perturbation theory methods known from quantum mechanics. Finally, we
perform a Monte Carlo study to estimate the surviving fraction of axion
miniclusters in the dark matter halo of our galaxy. We find that the reaction
to perturbations and the survival probability depend crucially on the density
profile. Weakly bound clusters are heated up and eventually destroyed, whereas
more strongly bound systems get even more compact as a result of perturbations
and are driven towards an axion star configuration.

Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology