In physics, the Lamb shift, named after Willis Lamb, is a difference in energy between two energy levels 2S1/2 and 2P1/2 (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy. Interaction between vacuum energy fluctuations and the hydrogen electron in these different orbitals is the cause of the Lamb shift, as was shown subsequent to its discovery. The Lamb shift has since played a significant role through vacuum energy fluctuations in theoretical prediction of Hawking radiation from black holes. This effect was first measured in 1947 in the Lamb–Retherford experiment on the hydrogen microwave spectrum and this measurement provided the stimulus for renormalization theory to handle the divergences. It was the harbinger of modern quantum electrodynamics developed by Julian Schwinger, Richard Feynman, Ernst Stueckelberg, Sin-Itiro Tomonaga and Freeman Dyson. Lamb won the Nobel Prize in Physics in 1955 for his discoveries related to the Lamb shift. Importance In 1978, on Lamb's 65th birthday, Freeman Dyson addressed him as follows: "Those years, when the Lamb shift was the central theme of physics, were golden years for all the physicists of my generation. You were the first to see that this tiny shift, so elusive and hard to measure, would clarify our thinking about particles and fields." Derivation This heuristic derivation of the electrodynamic level shift follows Theodore A. Welton's approach. The fluctuations in the electric and magnetic fields associated with the QED vacuum perturbs the electric potential due to the atomic nucleus. This perturbation causes a fluctuation in the position of the electron, which explains the energy shift. The difference of potential energy is given by Since the fluctuations are isotropic, So one can obtain The classical equation of motion for the electron displacement (δr) induced by a single mode of the field of wave vector and frequency ν is and this is valid only when the frequency ν is greater than ν0 in the Bohr orbit, . The electron is unable to respond to the fluctuating field if the fluctuations are smaller than the natural orbital frequency in the atom. For the field oscillating at ν, therefore where is some large normalization volume (the volume of the hypothetical "box" containing the hydrogen atom). By the summation over all This result diverges when no limits about the integral (at both large and small frequencies).