Group Properties of Hydrogenic Radial Functions

The radial wave functions of hydrogen are put into such a form that they form bases for irreducible unitary representations of an algebra isomorphic to that of $O(2,1)\mathrm{}$. Operators proportional to $r^k$ are found which form bases for the adjoint representations of this algebra. Matrix elements of these operators are evaluated, and selection rules are determined by considering Kronecker products of representations of $O(2,1)\mathrm{}$. Differences between this approach and one previously suggested are discussed.