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Encyclopedia > Lamb shift

In physics, the Lamb shift, named after Willis Lamb, is a small difference in energy between two energy levels $2 s 1 / 2$ and $2 p 1 / 2$ of the hydrogen atom in quantum mechanics. According to Dirac and Schrödinger theory, hydrogen states with the same $n$ and $j$ quantum numbers but different $l$ quantum numbers ought to be degenerate. The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... Willis Eugene Lamb, Junior (b. ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ... depiction of a hydrogen-1 atom showing the Van der Waals radius and the proton nucleus. ... Fig. ...

Experimental work

In 1947 Lamb and Robert Retherford carried out an experiment using microwave techniques to stimulate radio-frequency transitions between $2 s 1 / 2$ and $2 p 1 / 2$ 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 of about 1060MHz of the $2 s 1 / 2$ level above the $2 p 1 / 2$ level. Microwave image of 3C353 galaxy at 8. ... Doppler broadening is a broadening of spectral lines due to thermal agitation. ...

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 quantized and as for the harmonic oscillator in quantum mechanics its lowest state is not zero. So there exist little zero-point oscillations that cause the electron to execute rapid oscillatory motions. The electron is kind of "smeared out" and the radius is changed by $r + δ r$ . In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic). ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... In quantum physics, the photon (from Greek Ï†Ï‰Ï‚, phÅs, meaning light) is the quantum of the electromagnetic field (light). ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... A harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement : where is a positive constant. ... Fig. ... ZERO.POINT is a science fiction television series in development that revolves around Teresa Harwell, a quantum physicist searching for zero-point energy and the drifter she believes has the keys to understanding it. ... Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ...

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: Atomic units (au) form a system of units convenient for electromagnetism, atomic physics, and quantum electrodynamics, especially when the focus is on the properties of electrons. ...

$langle E_mathrm{pot} rangle=-frac{Ze^2}{4piepsilon_0}leftlanglefrac{1}{r+delta r}rightrangle.$

The Lamb shift itself is given by

$Delta E_mathrm{Lamb}=alpha^5 m_e c^2 frac{k(n,0)}{4n^3} mathrm{for} ell=0,$

with $k (n,0)-$ around 13 varying slightly with $n$ , and

$Delta E_mathrm{Lamb}=alpha^5 m_e c^2 frac{1}{4n^3}left[k(n,ell)pm frac{1}{pi(j+frac{1}{2})(ell+frac{1}{2})}right] mathrm{for} ellne 0 mathrm{and} j=ellpmfrac{1}{2},$

with $k(n,ell)$ a small number (< 0.05).

Category: Quantum field theory

Results from FactBites:

The Lamb Shift (709 words)
	In 1951, Willis Lamb discovered that this was not so - that the 2p(1/2) state is slightly lower than the 2s(1/2) state resulting in a slight shift of the corresponding spectral line (the Lamb shift).
	While the Lamb shift is extremely small and difficult to measure as a splitting in the optical or uv spectral lines, it is possible to make use of transitions directly between the sublevels by going to other regions of the electromagnetic spectrum.
	When the Lamb shift was experimentally determined, it provided a high precision verification of theoretical calculations made with the quantum theory of electrodynamics.

Willis Lamb (320 words)
	In 1955 Lamb won the Nobel Prize for physics "for discoveries concerning the fine structure of the hydrogen spectrum" that led to refinements of the quantum theories of electromagnetic phenomena.
	Lamb received his B.S. in Chemistry in 1934 at the University of California at Berkeley then went on to earn a Ph.D. in physics in 1938, having carried out his doctoral research on the electromagnetic properties of nuclear systems, working under the direction of Robert Oppenheimer.
	Lamb spent the next twelve years teaching physics at Yale, and then, in 1974 he accepted a position as professor of physics and optical sciences at the University of Arizona.

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Experimental work