Advances in modern laser technology allow for the generation of ultrashort (fewcycles) intense (I>10**14 W/cm2) laser pulses. Interaction of such intense pulses with molecules leads to Molecular High Order Harmonic Generation , Molecular Above Threshold Ionization , through the highly nonlinear nonperturbative response of electrons .The resulting harmonics are in fact the only current source of coherent attosecond (asec) pulses . Since the electron orbit period in the hydrogen atom is 152 asecs, such pulses are the preferred future tools for imaging, visualizing and controlling electron motion in molecules . Numerical solutions of multidimentional molecular Time-Dependent Schroedinger equations (TDSE) coupled to the photon Maxwell equation on multiprocessor parallel supercomputers are the essential mathematical tools for modelling and simulating the generation of asec pulses .These asec pulses are then used through molecular TDSE simulations to create Molecular Electron-Wavepackets (MEWP). The generation of MEWP, the study of their intrinsic properties and their manipulation are therefore the source of a new science- Attosecond Science, ie, the ultimate control of electrons in matter.
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