Test-Bed Simulations of Collisionless, Self-Gravitating Systems Using   the Schr\"odinger Method
  The Schr\"odinger Method is a novel approach for modeling numerically self-gravitating, collisionless systems that may have certain advantages over N-body and phase space methods. In particular, smoothing is part of the dynamics and not just the force calculation. This paper describes test-bed simulations which illustrate the viability of the Schr\"odinger Method. We develop the techniques necessary to handle ``hot'' systems as well as spherically symmetric systems. We demonstrate that the method can maintain a stable, equilibrium star cluster by constructing and then evolving a Plummer sphere. We also consider nonequilibrium initial conditions and follow the system as it attempts to reach virial equilibrium through phase mixing and violent relaxation. Finally we make a few remarks concerning the dynamics of axions and other bosonic dark matter candidates. The Schr\"odinger Method, in principle, provides an exact treatment of these fields. However such ``scalar field'' simulations are feasible and warrented only if the deBroglie wavelength of the particle is comparable to the size of the system of interest, a situation that is almost certainly not the case for axions in the Galaxy. Therefore the Schr\"odinger Method treats axions in the same way as other collisionless particles. We challenge recent claims in the literature that axions in the Galaxy form soliton stars. 
George Davies and Lawrence M. Widrow