Correspondence between classical and quantummechanical Boltzmann equations

To compare quantummechanical and classical Boltzmann equations for molecular gases, a correspondence is proposed for functions of angular momentum. Equivalence between irreducible tensors of both kinds is prescribed in a unique way by demanding that trace-averages of binary operator products be equal to solid-angle averages of products of the classical equivalents. Application to the linearized Waldmann-Snider equation for rigid linear molecules leads to an equivalent system for a set of functions φ_j(r, υ, ω, t), j = 0, 1, 2,…. If the quantum number j is approximated by a continuous variable, the system goes over into a single classical equation.