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Why is there only 1 peak in the NMR diagram? I've been told it's because they are in identical chemical environments, but how does that explain why there is only 1 peak?
Based on the reasoning used to derive the $n+1$ rule, it seems like there should be a quartet. The protons on the right can have spins states like (uud,ddd,udd,...) which can create a magnetic field that interacts with the external magnetic field. This new net magnetic field should change the energy between the 2 spin state energy levels of the protons on the left and thus changes the shift.
So why does it not?