Lm. Widrow et N. Kaiser, USING THE SCHRODINGER-EQUATION TO SIMULATE COLLISIONLESS MATTER, The Astrophysical journal, 416(2), 1993, pp. 120000071-120000074
A new numerical technique for following the evolution of collisionless
matter under the influence of gravity is proposed. Matter is modeled
as a Schrodinger field obeying the coupled Schrodinger and Poisson equ
ations. The de Broglie wavelength, lambda(deB), associated with this f
ield enters as a free parameter and is tuned according to the specific
ations of the simulation one is doing. In the limit lambda(deB) --> 0
(a limit which would require infinite computing power) the equations r
educe to the coupled Vlasov and Poisson equations as they should. Our
method can handle multiple streams in phase space and is competitive i
n terms of computation time with particle-mesh N-body simulations. Res
ults from a simple one-dimensional collapse of a self-gravitating obje
ct as well as a two-dimensional simulation of a cold dark matter unive
rse are used to illustrate the viability of the technique.