%0 Journal Article
%T Numerical solution of the non-linear Schrodinger equation using smoothed-particle hydrodynamics
%A Philip Mocz
%A Sauro Succi
%J Physics
%D 2015
%I arXiv
%X We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the non-linear Schrodinger equation in the Madelung formulation. The probability density of the wavefunction is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a novel, robust discretization is found. We demonstrate our numerical method on a variety of numerical test problems involving the simple harmonic oscillator, Bose-Einstein condensates, collapsing singularities, and dark matter halos governed by the Gross-Pitaevskii-Poisson equation. Our method is conservative, applicable to unbounded domains, and is automatically adaptive in its resolution, making it well suited to study problems with collapsing solutions.
%U http://arxiv.org/abs/1503.03869v1