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A derivation is here: http://en.wikipedia.org/wiki/Lamb_shift#Derivation or in Landau-Lifshitz. Bethe's original derivation is found e.g. in Matt Schwartz's Harvard lecture here http://isites.harvard.edu/fs/docs/icb.topic792163.files/20-LambShift.pdf The leading contribution to the Lamb shift is the one-loop level (the first non-classical ...


This is incorrect. The Lamb shift makes the $2\,{}^2 P_{1/2}$ state lower than the $2\,{}^2 S_{1/2}$; as such, the former will not spontaneously decay into the latter. In any case, these are states within the $n=2$ shell, so that their main decay channel is to the ground state, $1\,{}^2S_{1/2}$; this can and will happen on a ~nanosecond timescale (i.e. slow ...

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