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The generalised 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 generalisation of the first relation, and the advantages which they hold for computational purposes are discussed. An earlier calculation of the electron impact ionisation 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.

Additional information

Authors: HEY J D, Forschungszentrum Jülich GmbH (KFA) (DE)
Bibliographic Reference: Article: American Journal of Physics, Vol. 61 (1993) No. 8, pp. 741-749
Record Number: 199311254 / Last updated on: 1994-11-29
Original language: en
Available languages: en