Absorption rate on a quantised EM field

[brunow]

I have this problem:
Consider the next state for the EM field: $|A\rangle=\frac{1}{\sqrt{N!}}\left ( \int e^{-k^2} \boldsymbol{a}^\dagger_{k,+} \right )^N |0\rangle$. There is a particle in the unique bound state for spherical potential $V(r)=-\delta ^\prime(r)/r$. for absorb a photon if the initial state for field is |A>? I was thinking use the Fermi golden rule but I can't figure out. Any advice?

 

[PeterDonis]

@brunow : I used magic moderator powers to edit your post to correct the inline LaTeX. The correct way to do inline LaTeX is to use ##, not $.