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 Schrödinger equation these two energy levels should only depend on the principal quantum number and should therefore have the same energy.

Related Topics:
Physics - Willis Lamb - Energy - Energy level - Hydrogen atom - Quantum mechanics - Schrödinger equation - Quantum number

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

Related Topics:
Robert Retherford - Microwave

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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

Related Topics:
One-loop effect - Quantum electrodynamics - Photon

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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

Related Topics:
Harmonic oscillator - Quantum mechanics - Zero-point

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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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