Total Angular Momentum of Many Particles

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SUMMARY

The discussion focuses on determining the total spin state for four electrons, specifically the s=0 state. It highlights the use of Clebsch-Gordan coefficients for combining two electrons and introduces Wigner 9j symbols for adding the angular momenta of four particles. The relationship between Clebsch-Gordan coefficients and 3j symbols, as well as the use of 6j symbols for three angular momenta, is also established as a foundational concept in quantum mechanics.

PREREQUISITES
  • Understanding of Clebsch-Gordan coefficients
  • Familiarity with angular momentum in quantum mechanics
  • Knowledge of Wigner 9j symbols
  • Concept of 3j and 6j symbols in quantum theory
NEXT STEPS
  • Study the application of Wigner 9j symbols in quantum mechanics
  • Explore the derivation and use of Clebsch-Gordan coefficients
  • Learn about the significance of 3j and 6j symbols in angular momentum addition
  • Investigate the implications of total spin states in quantum systems
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Quantum physicists, students of quantum mechanics, and researchers focusing on angular momentum and spin states in multi-particle systems.

andrewm
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Hi,

How does one find the s=0 state for the addition of the spin of 4 (for example) electrons?

More generally, how does one obtain the total spin of 4 electrons?

I understand that for 2 electrons one can read the s=1 and s=0 states from a table of Clebsch-Gordan coefficients.
 
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To add 4 angular momenta, you can use something called Wigner 9j symbols. (Clebsch-Gordon coefficients are related to what are called 3j symbols; adding 3 angular momenta takes 6j symbols.)
 

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