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

In summary, there is a strong relationship between the concept of multiplets in group theory and the multiplet as a spin state of a system of particles. This is because group representations, specifically the SU(2) group representation for proper rotations in spacetime, play a crucial role in understanding quantum theory and the properties of composite systems, including spin. This relationship can be further explored in detail by studying Ballentine ch7.
  • #1
valleyman
26
0
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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  • #2
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.
 
  • #3
spin in non-rel. qm is just a physical property of the SU(2) group
 

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

What are multiplets in group theory?

Multiplets in group theory refer to a set of energy levels or states that have the same energy but differ in other quantum numbers.

How are multiplets classified in group theory?

Multiplets are classified based on the symmetry of the molecule or system. They can be either symmetric or antisymmetric.

What is the significance of multiplets in group theory?

Multiplets provide a way to understand the behavior of molecules and systems in terms of their symmetries, and help to predict their properties and interactions.

What are some types of multiplets in group theory?

Some common types of multiplets include singlets, doublets, triplets, quartets, and quintets. These refer to the number of states or energy levels within a multiplet set.

How are multiplets represented in group theory?

Multiplets can be represented using diagrams, such as energy level diagrams or symmetry diagrams, to visualize the different states and their symmetries.

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