Lamb shift

In physics, the Lamb shift, named after Willis Lamb, is a small difference of energy between two energy levels 2s_{1/2} and 2p_{1/2} of the hydrogen atom in quantum mechanics. According to the non relativistic Schr?dinger equation these two energy levels should only depend on the principal quantum number and should therefore have the same energy.

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In 1947 Lamb and Robert Retherford carried out an experiment using microwave techniques to stimulate radio-frequency transitions between

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2s_{1/2} and 2p_{1/2} levels. By using lower frequencies than for optical transitions the Doppler broadening could be neglected (Doppler broadening is proportional to the frequency). The energy difference Lamb and Retherford found was a rise

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of about 1060MHz of the 2s_{1/2} level above the 2p_{1/2} level.

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This particular difference is a one-loop effect of quantum electrodynamics, and can be interpreted as the influence of virtual photons that have been emitted and re-absorbed by the atom. In quantum electrodynamics (QED) the electromagnetic field is quantised

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and as for the harmonic oscillator in quantum mechanics its lowest state is not zero. So there exist little zero-point oscillations

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that cause the electron to execute rapid oscillatory motions. The electron is kind of "smeared out" and the radius is changed

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by r+delta r.

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The Coulomb potential is therefore perturbed by a small amount and the degeneration of the two energy levels is removed. The new potential can be approximated (using Atomic units) as follows:

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:langle E_mathrm{pot} angle=-rac{Ze^2}{4piepsilon_0}leftlanglerac{1}{r+delta r} ight angle.

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The Lamb shift itself is given by

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:Delta E_mathrm{Lamb}=lpha^5 m_e c^2 rac{k(n,0)}{4n^3} mathrm{for} ell=0,

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and

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:Delta E_mathrm{Lamb}=lpha^5 m_e c^2 rac{1}{4n^3}left mathrm{for} ell e 0 mathrm{and} j=ellpmrac{1}{2},

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with k(n,ell) a small number (

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Physics: Physics (from the Greek, φυσικός (phusikos), "natural", and φύσις (phusis), "nature") is the science of the natural world in the broadest sense, dealing with matter and energy and the fundamental forces of nature that govern the interaction...

Willis Lamb: Willis Eugene Lamb, Junior (b. July 12, 1913) is a physicist who won the Nobel Prize in Physics in 1955 "for his discoveries concerning the fine structure of the hydrogen spectrum". Lamb and Polykarp Kusch were able to precisely determine certain electromagnetic properties of the electron. See Lamb...

Energy: Energy is a fundamental quantity that every physical system possesses. Energy of physical system in a certain given state is defined as the amount of work W needed to change the state of the system from some initial state (called reference state or reference level) to the given state....

Lamb shift related Images and Photos (experimental)

Lamb	Shift 2	Late Shift, The (DVD)	Night Shift (DVD)
Swing Shift (DVD)	The Shift DVD	Lamb of God: Sacrament	Lamb of God: Sacrament
The Pet Lamb	Little Lamb and Ladybug	"Fringe Multi Glyph ""Shift"" EXCLUSIVE Mouse Pad"	The Passover Lamb