Development of algorithms for numerical resolution of Schrödinger equation in time


UCL Promotor : Bernard Piraux

UCL Collaborators :  Aliou Hamido

External collaborations : Javier Madroñero (U. München), Laurence Malegat (U. Orsay), Francisca Da Mota Furtado (U. London) and Patrick O'Mahony (U. London)

Funding : Cost Action CM0702

We develop two algorithms to solve the time-dependent Schrödinger equation that describes the partial and full fragmentation of driven three-body Coulomb systems. We consider in particular, the single and double ionisation of helium by electron and few photon impact. The algorithms are of spectral type and involve a time propagation of the full wave packet of the system by means of Arnoldi's method. The extraction of the information from the wave packet is based on the two following methods. The first one is the hyperspherical R-matrix approach with semi-classical outgoing waves. In that case, the wave packet is propagated semi-classically in space over extremely large distances until it reaches a region where all fragmentation channels are fully decoupled. The second method is based on a time-dependent scaling of the wave packet. In this conditions, the wave packet stays confined in the configuration space and its time evolution can be studied over very long periods of time.