Electronic states central force system

Two central problems remain. One is that one needs the potential which governs the motion. In many-atom systems, even if the motion is confined to the ground electronic state, this potential is a function of the spatial configuration of all the atoms. It is therefore a function of many variables, so its analytical form is far from obvious, nor do we necessarily want to know it everywhere. Indeed, we really only want it at each point along the actual trajectory of the system (so that the forces can be computed and thereby the next point to which the system will move to can be determined). Such an approach has been implemented [25] and applied to many-atom systems, and an extension to a multi-electronic state dynamics will be important... 

In many atomic systems there are other quantities besides the energy which take on definite values in the stationary states. Thus for an electron in a central field of force the square of the angular momentum of its orbital motion is such a quantity, having as possible values with I zero or a... 

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