How to calculate total cross section from differential cross section

[svletana]

I was doing the calculations for this: http://fermi.la.asu.edu/PHY531/cylinder/index.html
But I can't figure out how to go from $\frac{d\sigma}{d\phi}$ to the total cross section. My guess was that you did the integral from $\phi=0$ to $\phi=2\pi$, but that's not helping since I can't tell either how they got the absolute value squared inside the sum..

Thanks for anyone who listens :)

 

[kuruman]

If you had to find the absolute value squared of the expression, what would you have to do? Answer: Multiply the summation by its complex conjugate. Do it, integrate and see what you get. Don't forget to use different dummy indices for the summations.

 

[svletana]

If you had to find the absolute value squared of the expression, what would you have to do? Answer: Multiply the summation by its complex conjugate. Do it, integrate and see what you get. Don't forget to use different dummy indices for the summations.

That helped a lot, thanks! I can see now how with that you can make the terms with cos(nx)*cos(mx) with m=/=n cancel when you integrate from them being orthonormal :) The rest is history, thank you very much again!