Understanding Quantum Numbers and Their Limits in Particle States

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SUMMARY

This discussion clarifies the concept of quantum numbers in relation to electrons in separate atoms. It establishes that while two identical particles cannot share the same quantum numbers, electrons in different atoms can have the same quantum numbers due to their non-localized states. The key takeaway is that the focus should be on defining the right quantum numbers, such as angular momentum and spin, rather than considering spatial distance to determine if a state is "empty."

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UndeniablyRex
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Correct me where I go wrong.

I understand two particles can not share the same quantum numbers, but electrons in separate atoms do share the same quantum numbers. Where's the limit? How far away from a particle do you have to be in order to be able to consider that state "empty"?

Thank you for any help
 
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UndeniablyRex said:
Correct me where I go wrong.

I understand two particles can not share the same quantum numbers, but electrons in separate atoms do share the same quantum numbers. Where's the limit? How far away from a particle do you have to be in order to be able to consider that state "empty"?

Thank you for any help

No, not really, electrons associated with different atoms have different quantum numbers, the thing is, position is not a good quantum number to use, since the state of the electron is in general, not localised, so it does not have a definite position.

So it is not really about 'how far away', but rather, more about finding the right quantum numbers to define the state of the system. So for example, if the angular momentum and spins of the electron states are well defined, then you should use those numbers for comparison, not the position
 

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