How Does the ΔS = 0 Selection Rule Arise?

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SUMMARY

The discussion centers on the ΔS = 0 selection rule, which dictates that transitions between singlet and triplet states are forbidden in quantum mechanics. The participants seek a quantum mechanical explanation for this rule, particularly in relation to electric dipole transitions. They highlight the role of spin-orbit coupling in allowing these transitions to occur, albeit with reduced probability due to singlet/triplet mixing. References to various academic resources, including Wikipedia and specific quantum mechanics textbooks, are provided for further exploration.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly selection rules.
  • Familiarity with electric dipole transitions and their significance in spectroscopy.
  • Knowledge of spin-orbit coupling and its effects on quantum states.
  • Basic grasp of mathematical formulations in quantum mechanics, such as the Pauli equation.
NEXT STEPS
  • Study the derivation of selection rules in quantum mechanics, focusing on ΔS = 0.
  • Examine the role of spin-orbit coupling in quantum transitions, particularly in singlet and triplet states.
  • Research electric dipole transitions and their mathematical representation in quantum mechanics.
  • Review the Pauli equation and its implications for spin interactions with electromagnetic fields.
USEFUL FOR

This discussion is beneficial for quantum physicists, students studying quantum mechanics, and researchers exploring the intricacies of atomic transitions and selection rules.

pfollansbee
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Exactly what the title says.

I know that there exists a selection rule that ΔS=0, but I cannot find a quantum mechanical explanation for these transitions being forbidden. I know that it has something to do with the electric dipole, but I have not been able to find anything explicit.

In reference to my earlier thread, I want to state mathematically why singlet->triplet transitions are forbidden and then use spin orbit coupling to show why these transitions still happen (though with less probability) due to singlet/triplet mixing.

My best clue so far:
http://en.wikipedia.org/wiki/Selection_rule#Electronic_spectra


Anything would be excellent, so I can get a better starting point. A section from a book would be preferable though so that I could cite it. I've looked in Sakurai, Blinder, and Atkins/Friedman so far with no luck.

Thanks again!
 
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Have a look how the spin couples to the EM field in the non-relativistic limit:
http://en.wikipedia.org/wiki/Pauli_equation
Try to estimate the relation of a d*E term (responsible for electric dipole transitions) to the Stern Gerlach term e.g. for visible light.
 

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