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\begin{document}

The lamb shift is due to quantization of the electromagnetic field.

More precisely, it is the electron interaction with zero-point energy
of the quantized electromagnetic field.

To first order, this is interactions like emission and absorption
of a photon. This is consistent if \( \triangle p\triangle x\sim \hbar  \) and \( \triangle E\triangle t\sim \hbar  \). Energy shifts are infinite...
wheeee.... The only thing that matters is energy differences, so the
infinities get subtracted.

The lamb shift is \( \triangle E=\frac{4}{3}\frac{e^{4}\hbar }{m^{2}c^{3}}ln(\frac{m_{e}c^{2}}{<|E_{n'}-E_{n}|>})|\Psi (0)|^{2} \). This is nonzero for s-wave states. This is about
\( 4*10^{-6}eV \) . so \( \nu _{lamb}=1040MHz \)

The lamb shift further splits \( 2p_{\frac{1}{2}} \) from \( 2s_{\frac{1}{2}} \)

\end{document}
