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{{More footnotes|date=November 2009}} | |||
{{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}} | |||
Revision as of 18:21, 24 March 2013
Template:More footnotes
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Electric dipole transition is the dominant effect of an interaction of an electron in an atom with the electromagnetic field.
Following,[1] consider an electron in an atom with quantum Hamiltonian , interacting with a plane electromagnetic wave
Write the Hamiltonian of the electron in this electromagnetic field as
Treating this system by means of 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 written as
Electric dipole transitions are the transitions between energy levels in the system with the Hamiltonian .
Between certain electron states the electric dipole transition rate may be zero due to one or more selection rules, particularly the 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 is written as
and describes magnetic dipole transitions.
Even smaller contributions to transition rates are given by higher electric and magnetic multipole transitions.
See also
References
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