Optical Theorem

1. Jan 5, 2010

david_clint

1. The problem statement, all variables and given/known data
Hi. For the question given (attachment) where does the factor of 2PI in the function for sigma come from in the first step because I don't get it in my working for the first step.

2. Relevant equations
see attachment

3. The attempt at a solution
I got sigma (without the 2PI) by changing variable to t =cos theta, thus integrating between minus and plus 1

and using m=n in the legendre polynomial,

so I am wondering if the 2PI came from integrating over the phi dependence as we are dealing with scattering from a radial potential?

I also need prodding in the right direction for the next step!

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Last edited: Jan 5, 2010
2. Jan 6, 2010

Avodyne

Yes, the 2pi comes from integrating over phi, and so there should be a 2pi in front of the integral sign in the last equation.

3. Jan 6, 2010

Thanks:)