# Schrodinger equation vs Feynman diagrams

If one wants to assess how an electron orbits in a hydrogen atom one uses the Schrodinger equation. Ditto for an electron in a magnetic well. However if one wants to assess how particles interact or decay one uses Feyman diagrams, amplitudehrons, or various formulae from Feynman diagrams. The latter is what we usually talk about in CERN or RHC experimental results.

Question: where does Schrodinger stop and Feynman diagrams start? Do we need both? Can I derive the hydrogen s,p orbital shapes from a Feynman diagram(s)?

An electron orbiting a proton is still an interaction; I guess the salient difference is the electron is fundamental and cannot decay. Here Schrodinger typically applies. But could one go Feynman? Both are dynamic over time ... Both seem to calculate probabilities of interaction, and yet have different purposes.

• @johnrennie Is interpreting the question as being "when do we need QFT as opposed to Schroedinger's equation?". I think this makes sense but you may want to reformulate the question. Note also that between the two there's Diraq equation. One partial answer would then be: when relativistic effects become important. – lcv Oct 10 '19 at 11:07

However the Schrodinger equation just takes for granted the classical form of the electrostatic potential energy, which brings to the second aspect I want to mention. If we just assume the PE is proportional to $$r^{-1}$$ then the Schrodinger equation gives us results that match experiment. However to explain why the PE has this form requires QFT. That is, even though we may not need to resort to QFT to describe the electronic structure of a molecule, QFT helps explain why the Schrodinger equation works.