Spin-Orbit Coupling: Positive & Negative Signs Explained

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SUMMARY

Spin-orbit coupling in multi-electron atoms exhibits both positive and negative signs due to the eigenvalues of the z component of spin angular momentum. The discussion highlights the relevance of the SO-Hamiltonian in understanding these signs. Group theory provides a framework for explaining the behavior of spin-orbit coupling, particularly in the context of quantum mechanics. This foundational concept is crucial for comprehending the interactions in atomic systems.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the SO-Hamiltonian
  • Knowledge of eigenvalues and eigenstates
  • Basic concepts of group theory
NEXT STEPS
  • Research the mathematical formulation of the SO-Hamiltonian
  • Study the implications of eigenvalues in quantum systems
  • Explore group theory applications in quantum mechanics
  • Investigate the role of spin-orbit coupling in multi-electron atoms
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Physicists, quantum mechanics students, and researchers interested in atomic interactions and the mathematical foundations of spin-orbit coupling.

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why does spin-orbit coupling have a positive and negative sign?
 
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What exactly are you referring to?
 
the spin orbit coupling in atoms that have more than one electron in modern physics...
 
That part was obvious but were you referring to a specific formula like the SO-hamiltonian or something?
 
no... sorry! my mistake! it's why does the z component of the spin angular momentum have a positive and negative sign?
 
You mean the eigenvalues, right...? Well, basically, group theory explains why...

Daniel.
 

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