Operational procedure for the determination of the matrix elements of the direction cosines for a rigid symmetrical rotator

Abstract

An operational procedure is presented for obtaining the matrix elements ( J′ K′ M′| λ Aα | JKM), where λ Aα is the direction cosine between the A-axis ( A = X, Y, Z) and the α-axis ( α = x, y, z) of a space-fixed XYZ reference frame and a body-fixed xyz reference frame used to describe the pure rotation of a rigid symmetrical rotator. Ψ( J, K, M) are the normalized symmetrical rotator wave functions.