Deriving Average Energy Function For A Classical DOF

[Bashyboy]

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?

 

[dextercioby]

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.

 

[Bashyboy]

Do you perhaps mean the absolute value of q?

 

[BvU]

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.