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Homework Help: Statistical Mechanics Math Problem

  1. Aug 6, 2011 #1
    I was reading the solution to a statistical mechanics problem and this showed up:


    S2N-1 = the area of the 2N-1 dimensional unit sphere.

    Could anyone shed some light on how these expressions equal each other, I am quite dumbfounded :(.
  2. jcsd
  3. Aug 8, 2011 #2
    my guess is that, assuming your domain of integration is a high dimensional 2n-ball and you're integrating over all of R^2n, setting the radius=1 yields the (2n-1)-volume of a fixed boundary, which in (2n-1)+1 spherical coordinates is a S^(2n-1) sphere. then product this with the remaining radial dimension you get back the original ball integral.
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