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== Theory ==
Consider an atom interact with electromagnetic radiation which produces an
publisher=Oxford University Press|isbn=978-0-19-850696-6}}</ref>:
{{NumBlk|:|<math> E(t) = |\textbf{E}_0| Re( e^{-i{\omega}t} \hat{\textbf{e}}_{rad} )</math>|{{EquationRef|1}}}}
with amplitude <math>|\textbf{E}_0|</math>, angular frequency <math>\omega</math> and polarization vector <math>\hat{\textbf{e}}_{rad}</math>. Note that the actual phase of wave should be <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. This is called dipole approximation, and this approximation
The Hamiltonian for this interaction is <math> H_I = e \textbf{r} \cdot \textbf{E}(t) </math>, analogous to the energy of a classical dipole in a electric field. [[Time-dependent perturbation theory]] is required for calculating the stimulate transition rate. However, the result can be summarized with Fermi's Golden rule:
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