Solution of the time-dependent Schrödinger equation using uniform complex scaling

Abstract

The formalism of complex rotation of the radial coordinate is studied in the context of time-dependent systems. The applicability of this method is discussed and illustrated with numerical examples involving atoms exposed to electromagnetic field pulses. Complex rotation proves to be an efficient tool to obtain ionization probabilities and rates. Although, in principle, any information about the system may be obtained from the rotated wave function by transforming it back to its unrotated form, a good description of the ionized part of the wave function is generally subject to numerical challenges. It is, however, found that the combination of complex rotation and Floquet formalism offers an alternative and promising possibility to retrieve the physical information.