Greatest accuracy in the |mn> state is |n| = m

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SUMMARY

The discussion centers on demonstrating that the greatest accuracy in the |mn> state occurs when |n| = m for the angular momentum operator M. It is established that for this condition, the components Mx and My equal zero. The non-commuting nature of Mx and My is highlighted, indicating their orthogonality. Understanding these relationships is crucial for grasping angular momentum in quantum mechanics.

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  • Quantum mechanics fundamentals
  • Angular momentum operators in quantum systems
  • Commutation relations in quantum mechanics
  • Orthogonality in vector spaces
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How do we show that the greatest accuracy in the |mn> state is |n| = m for the Mx and My components?
 
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If M is an angular momentum operator, then Mx and My =0 for |n|=m.
 
Yes M is an angular momentum operator. I also know that the components Mx and My do not commute. However, I do not understand how to show the greatest accuracy.

Are you saying that Mx and My are orthogonal since they do not commute?
 

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