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  1. The laws of physics that apply at the molecular scale are the laws of quantum mechanics. Whereas quantum electronic structure calculations are now routine for the most part, “quantum dynamics” calculations of nuclear motion are still plagued with the “curse of dimensionality.” Similar challenges may apply to the emerging field of electron dynamics. In this article, the role of recent phase- space (PS) based methods is reviewed—both individually in comparison with each other, and also collectively as an avenue for lifting the above “curse.” In addition: (a) the oldest such PS method is revamped, in order to render it suitable for extremely high accuracy applications; (b) a new PS method designed for electron dynamics is applied to a calculation of the He atom—performed in full quantum dimensionality, and treating electron correlation exactly. 
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