How Are Multiplets in Group Theory Related to Spin States in Quantum Mechanics?

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SUMMARY

The relationship between multiplets in group theory and spin states in quantum mechanics is established through the study of group representations. Specifically, the SU(2) group is fundamental in understanding spin properties in non-relativistic quantum mechanics. The classification of elementary particles and the properties of composite systems are effectively analyzed using these group theoretical concepts. For a detailed exploration, refer to Chapter 7 of "Quantum Mechanics: A Modern Development" by Ballentine.

PREREQUISITES
  • Understanding of group theory, particularly SU(2) representations
  • Familiarity with quantum mechanics concepts, especially angular momentum
  • Knowledge of elementary particle classification
  • Basic principles of composite systems in quantum physics
NEXT STEPS
  • Study "Quantum Mechanics: A Modern Development" by Ballentine, focusing on Chapter 7
  • Research group representations in quantum mechanics
  • Explore the role of SU(2) in angular momentum and spin states
  • Investigate the classification of elementary particles using group theory
USEFUL FOR

Physicists, quantum mechanics students, and researchers interested in the interplay between group theory and quantum spin states.

valleyman
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hello, does anyone know what relationship exists, if exists, between the concept of multiplets in group theory and the multiplet as spin state of a system of particles?
Thanks,
valleyman
 
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valleyman said:
hello, does anyone know what relationship exists, if exists, between the concept of multiplets in group theory and the multiplet as spin state of a system of particles?

Absolutely. A large amount of quantum theory, classification of
elementary particles, and properties of composite systems is now well
understood by studying group representations. To see how this works
in detail for angular momentum, try Ballentine ch7.
 
spin in non-rel. qm is just a physical property of the SU(2) group
 

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