Umkehr effect: Difference between revisions

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{{More footnotes|date=November 2009}}
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{{Quantum mechanics}}
 
'''Electric dipole transition''' is the dominant effect of an interaction of an [[electron]] in an [[atom]] with the [[electromagnetic field]].
 
Following,<ref>http://electron6.phys.utk.edu/QM2/modules/m10/time.htm</ref> consider an electron in an atom with quantum Hamiltonian <math> H_0 </math>, interacting with a plane electromagnetic wave
 
: <math> {\mathbf E}({\mathbf r},t)=E_0 {\hat{\mathbf z}} \cos(ky-\omega t), \ \ \ {\mathbf B}({\mathbf r},t)=B_0{\hat{\mathbf x}} \cos(ky-\omega t). </math>
 
Write the Hamiltonian of the electron in this electromagnetic field as
 
<math> H(t) \ = \ H_0 + W(t). </math>
 
Treating this system by means of [[Perturbation theory (quantum mechanics)#Time-dependent perturbation theory|time-dependent perturbation theory]], one finds that the most likely transitions of the electron from one state to the other occur due to the summand of <math> W(t) </math> written as
 
: <math> W_{DE}(t) = \frac{q E_0}{m\omega}  p_z \sin \omega t. \, </math>
 
'''Electric dipole transitions''' are the transitions between energy levels in the system with the Hamiltonian <math> H_0 + W_{DE}(t) </math>.
 
Between certain electron states the electric dipole transition rate may be zero due to one or more [[selection rule]]s, particularly the [[Selection rule#Angular momentum|angular momentum selection rule]]. In such a case, the transition is termed ''electric dipole forbidden'', and the transitions between such levels must be approximated by ''higher-order transitions''.
 
The next order summand in <math> W(t) </math> is written as
 
: <math> W_{DM}(t) = \frac{q}{2m} (L_x + 2S_x) B_0 \cos \omega t \, </math>
 
and describes [[magnetic dipole transition]]s.
 
Even smaller contributions to transition rates are given by higher electric and magnetic multipole transitions.
 
==See also==
*[[Dipole]]
*[[Electric dipole moment]]
*[[Electromagnetism]]
 
== References ==
{{Reflist}}
 
[[Category:Quantum mechanics]]
 
 
{{physics stub}}

Latest revision as of 14:10, 28 October 2014

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