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Suppose you have some Lagrangian describing a system. Lets say two electrons, with an interaction. How would you go about finding say, the "force" on either particle, or the potential. Even in approximation? What method should I even begin to learn about?

I guess my problem is I understand whats in these density equations, but how do we convert that to anything usable, for things as simple as two electrons? So I'm looking for more methods, than description of the system.