# How to calculate scattering aplitude?

1. May 7, 2017

### Boris

1. The problem statement, all variables and given/known data
Hello, everyone . My teacher has given me an assignment to show that the exact Coulomb amplitude (2) satisfies the unitary condition for an elastic Scattering theory (1).

(1) $Imf(k',k'')=( \frac {κ} {4\pi} ) ∫ f^*(k',k'')f(k',k'')dΩ$

(2) $f(θ)= \frac {-α} {2mϑ^2} \frac{\Gamma(1+in)}{\Gamma(1-in)} \frac{\exp(-2in\ln\sin(\frac{\theta}{2}))}{\sin^2\frac{\theta}{2}}$

2. Relevant equations
As I understood the goal is to show that this condition is suitable for scattering in every potential including weak Coulomb potentional, right?

3. The attempt at a solution
That is why I took the formula (1) which combines Im part of amplitude with the whole amplitude and subtract Coulomb amplitude (2) . The problem is that we haven't studied Quantum mechanics yet, so it seems kinda difficult. I'm not asking you to show me every step of this calculation , but can you just give me any sort of advice how to start it ? Thank you in advance.

2. May 12, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.