Solving Homework: Sigma w/ 2PI from Radial Potential?

In summary, the factor of 2PI in the function for sigma comes from integrating over the phi dependence in the scattering from a radial potential. This leads to a 2pi in front of the integral sign in the last equation.
  • #1
david_clint
4
0

Homework Statement


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.

Homework Equations


see attachment

The Attempt at a Solution


I got sigma (without the 2PI) by changing variable to t =cos theta, thus integrating between minus and plus 1and 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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  • #2
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
Avodyne said:
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.

Thanks:)
 

What is "Solving Homework: Sigma w/ 2PI from Radial Potential"?

"Solving Homework: Sigma w/ 2PI from Radial Potential" refers to the process of determining the value of the variable sigma (σ) when using the radial potential function with 2π as the constant. This is a common task in physics and mathematics homework problems.

Why is it important to solve for sigma in this context?

Solving for sigma allows us to find the specific solution for a given problem using the radial potential function. It helps us understand the behavior and properties of the system being studied.

What are the steps for solving this type of homework problem?

The first step is to identify the given information, such as the values of the constant 2π, the potential function, and any other relevant parameters. Next, the equation for the radial potential function should be set up with the given values plugged in. Then, algebraic manipulation can be used to isolate and solve for sigma. Finally, the solution should be checked for accuracy and reasonableness.

What are some common challenges when solving for sigma in this context?

One common challenge is making algebraic mistakes, such as incorrect distribution or combining like terms. Another challenge can be understanding the meaning and significance of the solution in the context of the problem. Additionally, some problems may require the use of advanced mathematical techniques or concepts to solve for sigma.

How can I improve my skills in solving homework problems involving sigma and radial potential?

Practice is key to improving your skills in solving these types of problems. It's also helpful to review and understand the underlying concepts and equations involved. If you're struggling, seeking help from a teacher, tutor, or online resources can also be beneficial.

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