Statistical Mechanics · Problem 6.26

Ideal Bose Systems — R. K. Pathria

Physics — Statistical Mechanics · rotator-three-degrees-freedom-partition-function

Problem

The rotational kinetic energy of a rotator with three degrees of freedom can be written as εrot=Mξ22I1+Mη22I2+Mζ22I3,\varepsilon_{\text{rot}} = \frac{M_\xi^2}{2I_1} + \frac{M_\eta^2}{2I_2} + \frac{M_\zeta^2}{2I_3}, where (ξ,η,ζ)(\xi, \eta, \zeta) are coordinates in a rotating frame of reference whose axes coincide with the principal axes of the rotator, while (Mξ,Mη,Mζ)(M_\xi, M_\eta, M_\zeta) are the corresponding angular momenta. Carrying out integrations in the phase space of the rotator, derive expression (6.5.41) for the partition function jrot(T)j_{\text{rot}}(T) in the classical approximation.

Related theory

Browse the problem library