We present an exact single-electron picture that describes the correlated electron dynamics in strong laser fields. Our approach is based on the factorization of the electronic wavefunction as a product of a marginal and a conditional amplitude. The marginal amplitude, which depends only on one electronic coordinate and yields the exact one-electron density and current density, obeys a time-dependent Schrodinger equation with an effective time-dependent potential. The exact equations are used to derive an approximation that is a step towards a general and feasible ab-initio single-electron approximation for molecules. The derivation also challenges the usual interpretation of the single-active electron approximation. From the study of model systems, we find that the exact and approximate single-electron potentials for processes with negligible two-electron ionization lead to a qualitatively similar dynamics, but that the ionization barrier may be explicitly time-dependent.
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