|
In physics, the Lamb shift is a small difference of energy between two energy levels <math>2s_{1/2}<math> and <math>2p_{1/2}<math> of the Hydrogen atom in quantum mechanics. According to the Schrödinger equation these two energy levels should only depend on the principal quantum number and should therefore have the same energy.
In 1947 Lamb and Retherford carried out an experiment using microwave techniques to stimulate radio-frequency transitions between
<math>2s_{1/2}<math> and <math>2p_{1/2}<math> 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 <math>2s_{1/2}<math> level above the <math>2p_{1/2}<math> level.
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
and as for the harmonic oscillator in quantum mechanics it's lowest state is not zero. So there exist little zero-point oszillations
that cause the electron to execute rapid oscillatory motions. The electron is kind of smeared out and the radius is changed
by <math>r+\delta r<math>.
The Coulomb potential is therefor perturbed by a small amount and the degeneration of the two energy levels is removed. The new potential can be approximated (using atomar units) as follows:
<math>=-\frac{Ze^2}{4\pi\epsilon_0}<\frac{1}{r+\delta r}><math>
The Lamb shift itself is given by:
<math>\Delta E_{Lamb}=\alpha^5 m_e c^2 \frac{k(n,0)}{4n^3} <math> for l=0
and
<math>\Delta E_{Lamb}=\alpha^5 m_e c^2 \frac{1}{4n^3}[k(n,l)\pm \frac{1}{\pi(j+\frac{1}{2})(l+\frac{1}{2})}]<math> for l<math>\ne<math>0 and j=l<math>\pm \frac{1}{2}<math>
with k(n,l) a small number (<0.05).
| 
