Atomic electron transition: Difference between revisions

Revision as of 02:09, 8 November 2023

Revision as of 02:10, 8 November 2023

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publisher=Oxford University Press|isbn=978-0-19-850696-6}}</ref> Note that the actual phase is <math> (\omega t - \textbf{k} \cdot \textbf{r}) </math>. However, in many cases, the variation of <math> \textbf{k} \cdot \textbf{r} </math> is small over the atom (or equivalently, the radiation wavelength is much greater than the size of an atom) and this term can be ignored. This is called the dipole approximation. The atom can also interact with the oscillating magnetic field produced by the radiation, although much more weakly.

The Hamiltonian for this interaction, analogous to the energy of a classical dipole in a electric field, is <math> H_I = e \textbf{r} \cdot \textbf{E}(t) </math>. The stimulated transition rate can be calculated using [[time-dependent perturbation theory]]. However, the result can be summarized with [[Fermi's Goldengolden rule]]:

<math display="block">

Rate \propto |eE_0|^2 \times | \lang 2 |