Irreducible Tensor Expansion of Solid Spherical Harmonic-Type Operators in Quantum Mechanics

Abstract

A method is proposed to derive the general one- and two-center expansions of quantum mechanical operators that are in the form of regular or irregular solid spherical harmonics of any integral degree. The expansions are expressed as couplings of irreducible spherical tensors. The physical nature of such coupling and the parallelism to vector addition are illustrated. Possible uses of such expansions in the evaluation of molecular integral and their reduction to simple, known expansions obtained from other methods are briefly discussed.