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I Rayleigh Counting of Modes

  1. Jan 15, 2017 #1
    My question stems form the section "How Many Modes in a Cavity?" in the following derivation of Rayleigh-Jean Law:
    http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html#c2"

    In here, they count the number of modes as represented by volume of an eighth of a sphere. What's the mathematical justification behind using a spherical volume? Also, I understand why they divided by 8 since the n's must be positive, but aren't the n's here also supposed to be integers only?
     
  2. jcsd
  3. Jan 15, 2017 #2
    We may be interested in the mode count within a sphere. It may relate to questions like how many modes have energy less that some particular value or other calculations.

    There is an error here introduced by pretending like the points have a uniform density when actually there are discrete grid points. It's an approximation. It's possible to make a more accurate expression. You might want to look at the first chapter of https://www.amazon.com/Statistical-Mechanics-Third-R-Pathria/dp/0123821886if you are interested.
     
    Last edited by a moderator: May 8, 2017
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