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On the time-dependent Hartree-Fock equations coupled with a classical nuclear dynamics. (English) Zbl 1011.81087

Summary: We prove a global-in-time existence and uniqueness result for the Cauchy problem in the setting of some model of molecular quantum chemistry. The model we are concerned with consists of a coupling between the time-dependent Hartree-Fock equations (for the electrons) and the classical Newtonian dynamics (for the nuclei). The proof combines semigroup techniques and the Schauder fixed-point theorem. We also extend our result in order to treat the case of a molecule subjected to a time-dependent electric field.

MSC:

81V55 Molecular physics
81V70 Many-body theory; quantum Hall effect
81V45 Atomic physics
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