Matrix-element calculations for hydrogenlike atoms

The method of factorization, together with the hypervirial theorem, is shown to be appropriate for calculating matrix elements of operators that are functions of r, between hydrogenic radial wave functions that may belong to different atoms. Some numerical results are tabulated for matrix elements of the form 〈n’l’‖${\mathit{r}}^{\mathit{k}}$‖nl〉. The expressions given are valid for both diagonal- and off-diagonal matrix-element calculations with no limitation on the values of the n and l quantum number or in the power of the operator, which can have either positive or negative values.