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Recent developments toward the production and laboratory use of pulses ofhigh intensity, and/or of very high frequency, and/or of ultrashort duration,make possible experiments which can produce time-resolved data on ultrafasttransformations involving motions of electrons. The formulation, quantitativeunderstanding and prediction of related new phenomena entail the possibility ofcomputing and applying solutions of the many-electron time-dependentSchroedinger equation, for arbitrary electronic structures, including thedominant effects of Rydberg series, of multiply excited states and of themulti-channel continuous spectrum. To this purpose, we have proposed andapplied to many prototypical cases the state-specific expansion approach(SSEA). (Mercouris, Komninos and Nicolaides, Adv. Quantum Chem. 60, 333(2010)). The paper explains briefly the SSEA, and outlines four of itsapplications to recently formulated problems concerning time-resolvedelectronic processes, where electron correlations are crucial. These are, 1)The time resolution of the decay of polyelectronic unstable states, 2) Theexcitation and decay of strongly correlating doubly excited states andatto-time-resolution of their geometries, 3) The time-resolved process offormation of the interference profiles of resonance states during thefemtosecond photoionization of Helium and Aluminum, and 4) The relative timedelay in the (2s,2p) photoionization of Neon by an attosecond pulse.

Quantum Chemistry on the time axis: electron correlations and rearrangements on femtosecond and attosecond scales