  Recent developments toward the production and laboratory use of pulses of
high intensity, and/or of very high frequency, and/or of ultrashort duration,
make possible experiments which can produce time-resolved data on ultrafast
transformations involving motions of electrons. The formulation, quantitative
understanding and prediction of related new phenomena entail the possibility of
computing and applying solutions of the many-electron time-dependent
Schroedinger equation, for arbitrary electronic structures, including the
dominant effects of Rydberg series, of multiply excited states and of the
multi-channel continuous spectrum. To this purpose, we have proposed and
applied 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 its
applications to recently formulated problems concerning time-resolved
electronic processes, where electron correlations are crucial. These are, 1)
The time resolution of the decay of polyelectronic unstable states, 2) The
excitation and decay of strongly correlating doubly excited states and
atto-time-resolution of their geometries, 3) The time-resolved process of
formation of the interference profiles of resonance states during the
femtosecond photoionization of Helium and Aluminum, and 4) The relative time
delay in the (2s,2p) photoionization of Neon by an attosecond pulse.
