USING THE SCHRODINGER-EQUATION TO SIMULATE COLLISIONLESS MATTER

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.