O(2, 1) and the Harmonic Oscillator Radial Function

Abstract

The radial functions of the three‐dimensional isotropic harmonic oscillator are shown to form bases for unitary representations of the noncompact group O(2, 1). The functions r^s are shown to transform simply under the action of the generators of this group. As a result, matrix elements of r^s can easily be evaluated. Selection rules on these matrix elements are obtained by studying Kronecker products of representations of O(2, 1).