Deriving Average Energy Function For A Classical DOF

Bashyboy
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Hello everyone,

The problem I am currently working is exactly what is given in this link: https://www.physicsforums.com/showthread.php?t=554243

However, I do not understand why we integrate between 0 and infinity. What is the motivation for doing so?
 
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It's because of the absolute value of c. You have no reason to consider negative c's, since the absolute value will cancel the integration.
 
Do you perhaps mean the absolute value of q?
 
Yes.
The result Steve writes blows up at minus infinity (if c>0), so the integral is not 0 at all: it doesn't exist.
That's because he omitted the | | .
E = c |q| can be integrated. From minus infinity to 0 is exactly the same as from 0 to infinity.
 

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