Undergrad Averge orbital distance of electrons

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Calculating the average distance of electrons in orbitals involves using wave functions to determine probabilities. The expectation value for the squared distance between orbitals can be calculated as ##(\vec r_2 - \vec r_1)^2##, which provides insights into the distribution of electron positions. It's noted that higher moments of the distribution can also be calculated for more detailed analysis. A key point discussed is that the average distance between two orbitals, <r1 - r2>, equals zero due to symmetry. Understanding these calculations is essential for deeper insights into electron behavior in quantum mechanics.
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Is there anyway to calculate average distance of electrons?
Summary: Is there anyway to calculate average distance of electrons?

I know that we use wave function for orbital to show the probability of finding but my question is there any way to calculate distance between orbitals or energy states?
 
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One can certainly calculate the expectation value for r2-r1
 
hutchphd said:
One can certainly calculate the expectation value for r2-r1
I suggest calculating ##(\vec r_2 - \vec r_1)^2## to make the result more interesting.
 
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Yes I should have explicitly said all powers thereof to get moments of the distribution...thank you.
 
I think the point mfb was making is that <r1 - r2> is zero by symmetry.
 
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