Mathematics – Analysis of PDEs
Scientific paper
2010-02-09
Mathematics
Analysis of PDEs
This work was supported by the Viennese Science Foundation (WWTF) via the project "TDDFT" (MA-45), the Austrian Science Founda
Scientific paper
The multiconfiguration methods are widely used by quantum physicists and chemists for numerical approximation of the many electron Schr\"odinger equation. Recently, first mathematically rigorous results were obtained on the time-dependent models, e.g. short-in-time well-posedness in the Sobolev space $H^2$ for bounded interactions (C. Lubichand O. Koch} with initial data in $H^2$, in the energy space for Coulomb interactions with initial data in the same space (Trabelsi, Bardos et al.}, as well as global well-posedness under a sufficient condition on the energy of the initial data (Bardos et al.). The present contribution extends the analysis by setting an $L^2$ theory for the MCTDHF for general interactions including the Coulomb case. This kind of results is also the theoretical foundation of ad-hoc methods used in numerical calculation when modification ("regularization") of the density matrix destroys the conservation of energy property, but keeps invariant the mass.
Mauser Norbert J.
Trabelsi Saber
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