- #1
logic smogic
- 56
- 0
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!
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!