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Partition function problem

  1. Nov 17, 2011 #1
    I need some help with this problem:

    Consider a diatomic molecule closed in a cubic container of volume [itex] V [/itex] which hamiltonian is:
    [tex]H=\frac{p_1^2}{2m}+\frac{p_2^2}{2m}+\frac{K}{2}| \vec r_2 - \vec r_1|^2[/tex]
    where [itex]\vec r_1, \vec r_2[/itex] are the positions of the two atoms.

    a) Find the partition function in the limit [itex]V \longrightarrow \infty[/itex].
    b) Find (also for [itex]V \longrightarrow \infty[/itex] and without using the equipartition theorem) the mean value of [itex]|\vec r_2 - \vec r_1|^2[/itex].

    In particular I have some problems evaluating the integral

    [tex]\frac{1}{N!h^{3N}}\int e^{- \beta H(\vec q, \vec p)} d\vec q \ d\vec p[/tex]

    Thanks!
     
    Last edited: Nov 17, 2011
  2. jcsd
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