Düsseldorf 2007 – wissenschaftliches Programm

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MO: Fachverband Molekülphysik

MO 42: Quantum Chemistry (Theory)

MO 42.2: Vortrag

Mittwoch, 21. März 2007, 11:45–12:00, 6D

On the matrix singularity problem in the variational Gaussian wave packet method — •Tomaž Fabčič, Jörg Main, and Günter Wunner — 1. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart

Variational solutions of the time-dependent Schrödinger equation are often based on Gaussian wave packets (GWP) as trial functions. The equations of motion for the time-dependent Gaussian parameters become ill-conditioned from time to time during the propagation, and this problem increases with the number of propagated GWP, leading to extremely small step sizes of the integration routines. On the other hand a sufficiently large number of GWP is necessary to obtain accurate results. The instabilities of the equations of motion are due to a temporary overcrowding of the set of GWP, making the set of linear equations that has to be solved after each time step of integration nearly singular. We present a novel method to overcome these numerical problems by subjecting the GWP to adequate inequality constraints, rendering the integration process orders of magnitude faster. The power of the method is demonstrated for a two dimensional non-integrable model potential.