Hannover 2010 – scientific programme

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A: Fachverband Atomphysik

A 2: Atomic Systems in External Fields I

A 2.6: Talk

Monday, March 8, 2010, 15:15–15:30, F 107

A canonical transforms approach to the numerical solution of time-dependent quantum wave equations — •Heiko Bauke and Christoph H. Keitel — Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg

The dynamics of quantum systems is governed by quantum wave equations, which are analytically tractable in rare cases only. Therefore, efficient numerical algorithms are a major tool for the investigation of quantum dynamical processes in atomic systems and others.

The Shannon sampling theorem induces limits that bound the performance of algorithms for the numerical propagation of quantum wave functions. Algorithms are fundamentally limited by the wave-function’s energy spectrum as well as its momentum spectrum. However, these spectra depend on the wave-function’s Hilbert-space representation and, therefore, the efficiency of numerical propagation schemes depends on the Hilbert-space representation. We demonstrate how canonical transforms may be utilized to transform the wave function into a space where it has energy and momentum spectra with reduced band width. This may increase the performance of numerical algorithms by up to several orders of magnitude. Our approach includes the so-called Kramers-Henneberger transform as a special case and puts forward modifications towards an improved numerical efficiency.

[1] Heiko Bauke and Christoph H. Keitel, Phys. Rev. E 80, 016706 (2009)