# Partition function problem

1. Nov 17, 2011

### merkamerka

I need some help with this problem:

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

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

In particular I have some problems evaluating the integral

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

Thanks!

Last edited: Nov 17, 2011