You solve this problem by completing the square, integrating by parts, and applying Gauss's Law using the Green's Function formalism of the Laplace Transform in the particle's k-space coordinate system. I'm disappointed that only one of you got this problem correct."

I'd be disappointed if this weren't easy for you. :-). I'm still learning. I'm very happy that it's been as relatively painless as it has thus far.

Cheers,
Scott.