FURTHER PROPERTIES OF HYDROGENIC WAVE-FUNCTIONS

The generalized and canonical momentum operators in spherical polar coordinates are derived and discussed, and the radial operators applied to the evaluation of the Heisenberg uncertainty relation for bound states of hydrogenic atoms. The two Pasternack relations, which connect the expectation values [r(k)] for values of k differing by an integer, are examined, as well as a generalization of the first relation, and the advantages which they hold for computational purposes discussed. An earlier calculation by the present author, of the electron impact ionization cross section for hydrogen atoms in the 2S metastable state, is compared with other experimental data from the literature. The calculation of the wavelengths of transitions between hydrogen-like levels in highly excited ions possessing a few additional, tightly bound, electrons is described and compared with experimental data.