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The zero-field energy levels here are averaged over hyperfine structure; $h$ is the Planck constant. Electron self-energy and vacuum polarization produce radiative corrections. Self-energy describes the bound Electron's radiative interaction with its own electromagnetic field. Precision predictions also include nuclear recoil and proton charge radius effects; assigning recoil terms to the reference or Lamb shift is convention-dependent. A finite proton charge radius changes binding independently of radiative effects.^[ref]

A vacuum-electric field “jiggling” picture motivates one contribution, not every hydrogen atom energy correction.

A quantum electrodynamics correction separates hydrogen atom levels such as $2s_{1/2}$ and $2p_{1/2}$ that coincide in the simplest model.

The Lamb shift measures an energy level displacement beyond a specified Dirac equation reference. In the point-proton, infinite-nuclear-mass Coulomb potential model, $2S_{1/2}$ and $2P_{1/2}$ share principal quantum number $n=2$ and total electronic angular momentum $j=1/2$, hence energy, despite differing orbital angular momentum values.^[ref]

The Lamb-Retherford experiment converts a small energy difference into a large detector change: prepare a long-lived quantum state, transfer population into a short-lived one, and read the surviving beam.

The root mean square radius of the proton charge distribution. Finite nuclear size changes hydrogen atom energy levels and enters precision predictions for the Lamb shift.^[ref]