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By Norbert J. (a-wien-wpi) Trabelsi, C. Bardos, F. Golse, N. Mauser and A. Gottlieb


L 2 analysis of the multi-configuration time-dependent Hartree-Fock equations. (English summary) Math. Models Methods Appl. Sci. 20 (2010), no. 11, 2053–2073.1793-6314 Summary: “The multi-configuration methods are widely used by quantum physicists/chemists for numerical approximation of the many electron Schrödinger equation. Recently, first mathematically rigorous results were obtained on the time-dependent models, e.g. short-in-time wellposedness in the Sobolev space H 2 for bounded interactions with initial data in H 2, in the energy space for Coulomb interactions with initial data in the same space, as well as global well-posedness under a sufficient condition on the energy of the initial data. 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 result 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 the mass invariant.

Year: 2013
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