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Homework Help: Statistical mechanics

  1. Aug 27, 2013 #1
    In a aislate system, the probability on a microcanonical state [tex]\Gamma[/tex] is

    [tex] p(\Gamma ) = 1/K [/tex] , if E<H<E + ΔE, and 0 on otherwise

    with [tex] K = \int_{\Gamma : E<H<E+ΔE} d \Gamma [/tex]

    a) Show that ΔE →0, then
    [tex] p(\Gamma) = \frac{\delta (E-H)}{\int_{\Gamma : H=E} \delta(E-H)} [/tex]

    b) Show that if use the change of variable [tex] \Gamma \to (X,a)[/tex], with [tex] X[/tex] are 6N-1 coordinates abaut the surface H=E, and a is a perpendicular coordinate to this surface at the point X, then

    [tex] \int_D \delta (E-H) d \Gamma = \int_{D_E} \frac{ d X}{ || \frac{dH}{d \Gamma}||}[/tex]

    The rules of this forums says that i says my tried, but, sincerly i dont idea abaut this problem, i think on Taylor for the question a), but i dont have result.
  2. jcsd
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