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My main question is how the heck do you integrate (x^2)(exp(-a*x^2)) this is making me crazy, in tried integration by parts but that doesn't work as you just end up with the exponential back which i can't integrate in the first place. U sub would also make me insane. If someone can explain how to integrate this evil thing i would really appreciate it. I am willing to use any method of integration people come up with.

Also am I right about the integrating over the respective amplitudes? All space does not make sense to me, as we are talking about the stretching of an atom and that does not stretch infinitely.

If anyone can help I would REALLY appreciate it,

thanks

rachael