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Trying to evaluate an integral. To be specific, I'm trying to find the expectation value of $x^2$ for the ground state of hydrogen. Here is the code I used:

FullSimplify[
  Integrate[x^2/(Pi*a^3) E^((-2 Sqrt[x^2 + y^2 + z^2])/a), {x,-Infinity, Infinity}]]

The odd part is it worked when I calculated $\left<x\right>$, i.e. just drop an $x$ from the first fraction.

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Did you try letting Mathematica know that $a$ is real, say with Assuming[] ? – Zet Jun 7 '14 at 15:21
    
Just did, no such luck:( – Sam Jun 7 '14 at 15:26
    
Then I'd try to convert the integral into spherical coordinates (although it is disappointing that M didn't try it). – Zet Jun 7 '14 at 15:44
    
Try a change of coordinate cartesian-spherical. – b.gatessucks Jun 7 '14 at 15:44
    
Yes, that turned out to be the proper way to do the problem anyway. – Sam Jun 7 '14 at 16:35

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