Proving Spin-1/2 Spinors are Eigenvectors to $\hat S^2$

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To prove that all spinors of a spin-1/2 particle are eigenvectors of \(\hat S^2\), one should start by demonstrating that the operators \(S_z\) and \(\hat S^2\) commute. This can be achieved using the principles of angular momentum theory. Once commutation is established, a significant theorem from functional analysis can be applied to derive the desired result. The discussion emphasizes that while the problem may seem complex, it can be straightforward with the right approach. Understanding the relationship between spin and angular momentum is crucial for this proof.
danja347
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Can anyone give me some hints? I need to prove that all spinors to a spin-1/2 particle are eigenvectors to \hat S^2!

/Daniel
 
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danja347 said:
Can anyone give me some hints? I need to prove that all spinors to a spin-1/2 particle are eigenvectors to \hat S^2!

/Daniel

What is spin?It's a weird form of angular momentum.
Use the theory of angular momentum to show that S_{z} and S^{2} commute then apply a monstruously important theorem of functional analysis to find your result.
 
dextercioby said:
What is spin?It's a weird form of angular momentum.
Use the theory of angular momentum to show that S_{z} and S^{2} commute then apply a monstruously important theorem of functional analysis to find your result.

That´s right. Sometimes a problem is very easy. Good Luck Daniel!
 

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