- #1

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**1. Problem**

Evaluate

[tex]\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} z^{2} e^{-A \sqrt{x^{2}+y^{2}+z^{2}}} dxdydz[/tex]

**2. Useful Formulae**

*none*

**3. Attempt at Solution**

Well, this is part of a much larger problem. I am trying to compute the dipole moment matrix elements for a Hydrogen 2P -> 1S transition, and it involves this integral. In particular, this is the "z-component" of the |2,1,0> -> |1,0,0> transition - I've already found the x- and y-components to be zero for this transition.

*I've spent nearly an hour looking through online integral tables, and I've found nothing useful.*Can anyone help? Thanks!