If 4 atoms are represented in three dimensions, with each particle having coordinates $(x,y,z)$, one can compute the rotations around their nucleus with the Rodrigues Rotation formula. I’m now left with the electric and magnetic forces between the particles to finally model mathematically all the particles. Is there any simple way which I can approach the issue with forces acting between particles without having to figure out many angles and partial derivatives to know how it will affect the trajectory of electrons and protons (I’m considering only hydrogen atoms)?

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    $\begingroup$ Not sure what you are trying to do. Are you modeling electrons orbiting the proton in H, or something more complex like and H-H bond? You start very general then say you only care about hydrogen, Just look up the hydrogen atom model in any QM book. $\endgroup$ – ggcg Aug 14 at 19:51

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