I'm struggling to understand degenerate perturbation theory. It's clear that in this case the 'normal' approximation method fails completely seeing as you get a divide by zero.(adsbygoogle = window.adsbygoogle || []).push({});

I follow the example for a two state system given in e.g D.J Griffiths "Introduction to Quantum Mechanics"

However, I don't understand the reasoning of how we go from that to say that we should generally "diagonalize the perturbation in the subspace of degenerate states" - how are wesurefrom the get go that the only significant contributions to the perturbed energy should come from the states which are degenerate in the original energy? Haven't we just completely excluded any others from consideration by this method?

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# I Degenerate Perturbation Theory

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