## 7 Conclusions  
Thanks to significant developments of the last two to three decades, both theory and experiment can now provide the same or complementary information and insight into attosecond-resolved electron dynamics associated with hyperfast electron rearrangements upon pulsed excitation of atoms and molecules into the continuum. As regards experiment, the novel techniques that have been developed and used for the study of such phenomena are discussed in the cited works [7; 8; 10; 11; 29]. As regards theory and computation, the formal construction, the credible solution, and the quantitative understanding of the related new types of TDMEPs require that the METDSE is treated and solved from a many-electron point of view, for closed- as well as for open-shell atomic or molecular states, rather than in terms of models or one-electron potentials. To this purpose, a fundamental requirement is for theory to account for the details of the electronic structures and the scattering continua of the states participating in the dynamics. The SSEA, whose main features were presented in Section 3, satisfies the above requirements [1; 2; 3; 4; 5; 6; 14; 15; 16; 21; 14; 16; 22]. Indeed, because of its structure, its implementation for each problem of interest can be easily understood, regardless of the wavelength(s) of the applied pulse(s), which can range from the IR to the x-ray region. In Sections 4-6, I discussed various types of TDMEPs whose solutions, with attosecond resolution, have provided quantitative information and good insight into hyperfast electron dynamics and their relation to state-specific self-consistent fields, electron correlations, interchannel couplings, and resonances. The results were obtained in terms of many-electron wave functions \(\Psi(t)\), calculated by solving the METDSE nonperturbatively via the SSEA. In addition, when the pulse is chosen to be short and relatively weak, it is possible to formulate and calculate perturbatively the time-resolved preparation and evolution of states in the continuum in terms of practical analytic formulas containing information about the characteristics of the pulses and the time delay between two pulses [16; 54; 63]. The cases that were brought to attention as examples were:  
1. The ab initio determination of the details of the time-resolved decay of autoionizing states via _one-electron tunneling_ or _two-electron rearrangements_, thereby identifying quantitatively the regimes of _nonexponential decay_ (NED) for states very close to threshold. I point out that the predictions for NED were made not only for the case of very long times [12; 13] but also for the case of very short times after the preparation of the N-electron decaying state [64]. The degree to which the preparation step affects the NED for each particular N-electron isolated decaying state might be a challenging question for attosecond physics. 2. The time-resolved coherent preparation and decay of strongly correlated doubly excited and inner-hole excited autoionizing states. (Prototypical cases of electron dynamics in helium and aluminum.) 3. The time-resolved identification of electron correlation _beats_ and correlation-induced geometrical rearrangements of electrons inside the atom, which occur on the attosecond scale. For molecules, such rearrangements may take also place interatomically. 4. The time-resolved generation of the energy profiles of doubly excited (helium) and inner-hole excited (aluminum) autoionizing states during photoionization by hypershort radiation pulses. The published figures explicitly and quantitatively depicted for the first time the time-dependent effects on these profiles of the interference between the localized and scattering components of these states. 5. The relative time delay in the photoemission of two electrons from different subshells of an atom (case of the (_2s,2p_) photoionization of neon).