The Calculation of Statistical Averages for Perturbed Systems

Abstract

A general expression is derived for the statistical mean value of any function of dynamical variables, averaged over all the molecules of a gas in the presence of external fields. This expression is in the form of a multiple Taylor's series in powers of $\frac{1}{\mathrm{kT}}$ and of the field strengths. Explicit formulas, valid for diatomic and polyatomic molecules, are given for the coefficients in this series, up to and including the cubic terms. The general formula is then applied in the solution of two specific problems: (1) Effect of a magnetic field on the electric susceptibility of a molecule. (2) Theory of the Kerr effect in diatomic and polyatomic molecules. The concluding sections give applications of the formulas developed in §1 to the perturbation theory of conservative and non-conservative systems.