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 well-posedness in the Sobolev space H2 for bounded interactions20 with initial data in H2, in the energy space for Coulomb interactions with initial data in the same space,25,5 as well as global well-posedness under a sufficient condition on the energy of the initial data.4,5 The present contribution extends the analysis by setting an L2 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 the mass invariant.
|Original language||English (US)|
|Number of pages||21|
|Journal||Mathematical Models and Methods in Applied Sciences|
|State||Published - Nov 2010|
Bibliographical noteFunding Information:
This work was supported by the Viennese Science Foundation (WWTF) via the project \TDDFT" (MA-45), the Austrian Science Foundation (FWF) via the Wissenschaft-kolleg \Di®erential equations" (W17) and the START Project (Y-137-TEC) and the EU funded Marie Curie Early Stage Training Site DEASE (MEST-CT-2005-021122).
- HartreeFock equations
- Multi-configuration methods
- Strichartz estimates
ASJC Scopus subject areas
- Modeling and Simulation
- Applied Mathematics