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Deriving Average Energy Function For A Classical DOF

  1. Apr 6, 2014 #1
    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. jcsd
  3. Apr 7, 2014 #2


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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.
  4. Apr 7, 2014 #3
    Do you perhaps mean the absolute value of q?
  5. Apr 8, 2014 #4


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    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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