## 2 Introduction  
In modern studies of the interaction of hypershort and/or strong radiation pulses for a large range of wavelengths with atoms and molecules, a desideratum of crucial importance is the possibility of extracting quantitative (i.e., not just descriptive) information and understanding about nonlinear processes for different wavelengths, (e.g., high-harmonics generation) or _time-resolved_ phenomena of hyperfast electron dynamics, where both the discrete spectrum and the multichannel continua, including resonance (autoionizing) electronic states, are involved. As regards theory, such information and understanding can become accessible via formal constructions and computational methods that can go beyond the level of phenomenology or one-electron models and solve a variety of TDMEPs on the _time axis_. This endeavor depends directly on the possibility of determining and using the time-dependent solution,\(\Psi(t)\), of the METDSE. The matter-field interaction contains the pulse characteristics of duration, shape, intensity, and frequency. If the many-electron \(\Psi(t)\) for a particular problem can be calculated accurately, its use within an appropriate theoretical construction allows the reliable description of the physics of interest, including, of course, quantitative predictions, the hallmark of any generally applicable theory. The same physics is obtainable via the appropriate measurement. For ordinary ground states of neutral atoms and molecules interacting with pulsed radiation, if the field is strong, say \(10^{12}\) to \(10^{13}\) W/cm\({}^{2}\) and above, and the pulse is hypershort, say in the range of attoseconds (_as_) to a few decades of femtoseconds (_fs_) (normally not too many cycles of the field), \(\Psi(t)\) must, in general, be obtained nonperturbatively, taking into account, correctly and systematically, the significance of each problem's contributions to the states of both the discrete and the continuous spectra. This criterion is satisfied by the SSEA, which is conceptually simple, yet general and transparent with respect to the interplay between dynamics and electronic structures and spectra. A brief description of this computational tool in the theoretical study of time-resolved electron dynamics is given in Section 3. For details, the reader is referred to [1; 2; 3] and their references. Implementation of the SSEA has allowed different types of TDMEPs to be solved, with quantitative results that can be compared with a variety of experiments. For example, see [4; 5] for results from the calculation and quantitative understanding of observables in the multiphoton ionization of helium by UV and EUV femtosecond pulses. Lest it is thought from the previous statement that the SSEA is limited to two-electron systems, I note that the applications include many-electron atoms and topics of multiphoton dissociation and association of diatomics, with initial-state wavefunctions being of the closed-shell as well as the open-shell type [1; 2; 3]. For example, the SSEA calculation of \(\Psi(t)\) (including state-specific correlations), allowed the quantitative prediction of the time-resolved creation during photoionization of the profiles of inner-hole autoionizing states of aluminum decaying into a multichannel continuum [6]. The significance of going beyond two-electron systems when attempting to solve the METDSE while taking into account the _state-specific_ self-consistent fields and electron correlations for any type of electronic structures was underlined in [6] as follows:  
_This is clearly a desideratum for experiment as well, if progress is to be characterized by new information on a variety of real systems. For example, only a small part of what one learns about control or about the effects of electron correlation from the experimental and/or theoretical studies of the interaction of the He \(1s^{2}\,^{1}S\) ground state with a strong electromagnetic pulse, can be transferred to other systems.