Deriving Average Energy Function For A Classical DOF

1. Apr 6, 2014

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?

2. Apr 7, 2014

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.

3. Apr 7, 2014

Bashyboy

Do you perhaps mean the absolute value of q?

4. Apr 8, 2014

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.