Numerical solution of the time-dependent Schrodinger equation for continuum states

The time-dependent Schrodinger equation is solved numerically by using fast -Fourier transforms (FFTs) to evaluate the integrating factor e((i/2)del2(t -t')) in the integral form of the Schrodinger equation. The need for bounda ry conditions at grid boundaries is obviated provided the grid box is large enough that V psi, on which the integrating factor operates, is bounded wi thin it. This means that psi can be represented as appropriately unbounded rather than as a wave packet confined within the box, whose spreading over time to the grid boundaries places practical Limits on the duration of the collision. This development means that numerical simulations for electron o r positron scattering can be carried out at lower momenta k < 1 than is cur rently practical using a wave packet description. (C) 2000 John Wiley & Son s, Inc.