Symmetrization of eigenfunctions of angular momentum in point groups

摘要

The eigenfunctions jm] of angular momentum can combine linearly to make basis functions of irreducible representations of point groups. We surmount the projection operator and find a new method to calculate the combination coefficients. It is proven that these coefficients are components of eigenvectors of some hermitian matrices, and, that far all pure rotation point groups, the coefficients can be made real numbers by properly choosing the azimuth angles of symmetry elements of point groups in the coordinate system. We apply the coupling theory of angular momentum to obtain the general formulas of the basis functions of point groups. By use of our formulas, we have calculated the basis functions with half-integers j from 1/2 to 13/2 of double-valued irreducible representations for the icosahedral group. (C) 2001 John Wiley & Sons, Inc. Int J Quantum Chem 83: 286-302, 2001. [References: 16]