## Abstract

The multiconfiguration time-dependent Hartree-Fock (MCTDHF for short) system is an approximation of the linear many-particle Schrödinger equation with a binary interaction potential by nonlinear "one-particle" equations. MCTDHF methods are widely used for numerical calculations of the dynamics of few-electron systems in quantum physics and quantum chemistry, but the time-dependent case still poses serious open problems for the analysis, e.g. in the sense that global-in-time existence of solutions is not proved yet. In this letter we present the first result ever where global existence is proved under a condition on the initial datum that it has to be somewhat close to the "ground state".

Original language | English (US) |
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Pages (from-to) | 147-152 |

Number of pages | 6 |

Journal | Applied Mathematics Letters |

Volume | 22 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2009 |

Externally published | Yes |

### Bibliographical note

Funding Information:This work was supported by the Austrian Ministry of Science via its grant for the WPI, by the Austrian Science Foundation (FWF) via the Wissenschaftkolleg “Differential equations” (W17) and the START Project (Y-137-TEC), by the WWTF (Viennese Science Fund, project MA-45), as well as by the EU funded Marie Curie project DEASE (contract MEST-CT-2005-021122).

## Keywords

- Few-electron systems
- Ground State
- Linear N-particle Schrödinger equation
- MCTDHF system

## ASJC Scopus subject areas

- Applied Mathematics