2010/02/09 by Norbert J. Mauser, Mauser, Norbert J., Saber Trabelsi +1
Chemistry · Mathematics · Physics and Astronomy · #34A12 #35Q40 #35Q41 #35Q55 #35Q70 #Advanced Mathematical Physics Problems #Advanced Physical and Chemical Molecular Interactions #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:34A12 #msc:35Q40 #msc:35Q41 #msc:35Q55 #msc:35Q70
paper · pdf · doi:10.48550/arxiv.1002.1816
This work was supported by the Viennese Science Foundation (WWTF) via the project "TDDFT" (MA-45), the Austrian Science Foundation (FWF) via the Wissenschaftkolleg "Differential equations" (W17) and the START Project (Y-137-TEC) and the EU funded Marie Curie Early Stage Training Site DEASE (MEST-CT-2005-021122)
arxiv created 2010/02/09 · openalex publication_date 2010/02/09 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The multiconfiguration methods are widely used by quantum physicists and 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 interactions (C. Lubichand O. Koch with initial data in H2, 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 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 invariant the mass.