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In the derivation of probability transition of time-dependent perturbation theory (see for example these notes, from Ben Simons from Cambridge University), I have only encountered treatments of non-degenerate systems, but the result seems independent of whether the system is degenerate or non-degenerate.

In time-independent perturbation theory, the need of treating the degenerate systems in a different way arises from the presence of energy differences present in the denominator of a certain quantity, the coefficients of the expansion of the perturbed eigenvectors. However here no divergence occurs and so I want to know, the derivation of the probability transition for discrete degenerate systems can be treated equivalently to that of non-degenerate systems?

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  • $\begingroup$ Minor comment to the post (v1): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. $\endgroup$ – Qmechanic Jan 5 at 9:15
  • $\begingroup$ What exactly are you looking for? Do you know Fermi’s golden rule? $\endgroup$ – InertialObserver Jan 5 at 20:25
  • $\begingroup$ @InertialObserver I do know the Fermi's Golden rule, my question was regarding transitions between degenerate discrete states like in an hydrogen atom, but your point is very good, thank you! $\endgroup$ – Alex Jan 7 at 8:09

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