Spin Observables: Defining Reference Axes

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SUMMARY

The discussion centers on defining reference axes in the context of spin observables, specifically addressing the relationship between the Pauli matrices \( S_x \), \( S_y \), and \( S_z \). The key conclusion is that the ladder operators \( S_{\pm} \) are defined as \( S_{\pm} \equiv S_x \pm iS_y \), which indicates their action is oriented along the z-direction. This establishes a clear criterion for reference axes in quantum mechanics.

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  • Understanding of quantum mechanics principles
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  • Basic grasp of ladder operators in quantum theory
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What is the criterion to define the reference axes, since $S_x$, $S_y$ and $S_z$ correspond to different Pauli matrices?
 
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I found the answer: In the theory the ladder operators are defined as

S_{\pm} \equiv S_x \pm iS_y.

That is, they act on the z direction.
 

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