Statistical Mechanics · Problem 4.7

Formulation of Quantum Statistics — R. K. Pathria

Physics — Statistical Mechanics · diatomic-molecules-grand-canonical

Problem

Consider a classical system of non-interacting, diatomic molecules enclosed in a box of volume

V

at temperature

T

. The Hamiltonian of a single molecule is given by

H(r_1, r_2, p_1, p_2) = \frac{1}{2m}(p_1^2 + p_2^2) + \frac{1}{2}K|r_1 - r_2|^2.

Study the thermodynamics of this system, including the dependence of the quantity

\langle r_{12}^2 \rangle

T