S-Matrix in non-relativistic limit

[nklohit]

I have a problem in deriving the formula :
\left \langle p^\prime | iT | p \right\rangle = -2\pi i\widetilde{ V}(q)\delta(E_{p^\prime}-E_{p})
which is in Peskin's QFT book. How to derive it?
Is there anything to do with \psi = e^{i\vec{k}\cdot\vec{r}}+\frac{f(\theta)}{r}e^{i\vec{k^\prime}\cdot\vec{r}} ?

 

[Meir Achuz]

The energy delta function comes from an integral of the exponential time factors in
\psi(r,t)~exp[i(E_p-E-p')].
The V(q) is the Fourier transform of the potential.

 

[nklohit]

Thank you :)