Averge orbital distance of electrons

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SUMMARY

The discussion focuses on calculating the average distance of electrons in atomic orbitals using wave functions. Participants emphasize the use of expectation values, specifically calculating the expression for \((\vec{r}_2 - \vec{r}_1)^2\) to derive moments of the distribution. It is noted that the average distance between orbitals, represented as , equals zero due to symmetry considerations. This highlights the probabilistic nature of electron positioning in quantum mechanics.

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Iceking20
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TL;DR
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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