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Global well-posedness for the MCTDHF equations

Saber Trabelsi


This note is devoted to the multi-conguration time-dependent Hartree-Fock (MCTDHF) equations for molecular systems with pairwise interaction. This set of coupled nonlinear PDEs and ODEs provides with an approximation to the N{particles time-
dependent Schrdinger equation. The approximation is based on (time-dependent) linear combinations of (time-dependent) Slater determinants. We present local-in-time existence and uniqueness of a solution to the associated Cauchy problem in
energy space (with Coulomb interaction). This solution is shown to be global-in-time under a full-rank assumption depending only on the initial data.


approximation, Cauchy problem .

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