Integration of the Schrödinger Equation on a Massively Parallel Processor

Abstract

The behavior of atoms in strong radiation fields depends critically upon the time evolution of the field. For example, it has been found1 that above-threshold ionization (ATI) spectra show radical changes as the duration of the exciting laser pulse decreases; there is also theoretical evidence2 for novel phenomena, such as population trapping, which occur only for relatively short pulses. In order to treat problems of this sort theoretically, one must employ methods that accommodate general time variation of the radiation field. The most direct such method is numerical integration of the time-dependent Schrödinger equation. This would be an entirely non-controversial approach if vast computational resources were not required to implement it in practice. To date there have been only a few reports3 of direct integration of the time-dependent Schrodinger equation for a three dimensional, one-electron atom in a radiation field.