http://hyperphysics.phy astr.gsu.edu/hbase/quantum/hydfin.html
http://hyperphysics.phy‐astr.gsu.edu/hbase/quantum/hydfin.html
The textbook treatment of the spin‐orbit correction for s
states clearly cannot be correct, since there is no orbital motion in such states Nevertheless the spin‐orbit
motion in such states. Nevertheless the spin
orbit formula formula
predicts exactly that same result as can be obtained from the so‐called Darwin term.
From Wikipedia.org:
This term modifies the effective potential of the nucleus. It affects only the s states, since all other states have probability amplitudes that vanish at the origin. It is b bilit
lit d th t
i h t th
i i It i
understood physically to arise from a smearing out of the interaction between the electron and nucleus due to relativistic effects that are built into the Dirac equation.
The Lamb shift affects only s states, similar to the Darwin term. However it is not predicted by the Dirac equation. One must quantize the electromagnetic field, leading to quantum electrodynamics. Then the Lamb shift results from vacuum fluctuations of the electromagnetic field, which modify the Coulomb potential of the nucleus.