Generalized Discrete-Continuum Radial Integrals with Coulomb Functions
- 1 June 1966
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 7 (6) , 955-959
- https://doi.org/10.1063/1.1705008
Abstract
Simple closed‐form computational formulas involving only elementary functions are obtained for the hydrogenic, discrete‐continuum matrix elements <k, l′ |rm| n, l>. The results allow for different effective charge parameters Z and Z′ for the discrete and continuum functions. The central radial integral computed is sufficiently general to allow the evaluation of matrix elements of rm exp(− r/ε) between the Coulomb continuum functions and any discrete function formed from rk exp(− r/A). Results are also given for the free‐particle limit as Z′ → 0.Keywords
This publication has 6 references indexed in Scilit:
- Generalized Radial Integrals With Hydrogenic FunctionsReviews of Modern Physics, 1964
- The Hydrogen Recombination SpectrumMonthly Notices of the Royal Astronomical Society, 1958
- Zur Quantenmechanik photoelektrischer ProzesseAnnalen der Physik, 1930
- Über den Photoeffekt in der K‐Schale der Atome, insbesondere über die Voreilung der PhotoelektronenAnnalen der Physik, 1930
- Zur Berechnung der Matrizen beim WasserstoffatomAnnalen der Physik, 1929
- Über den Stoß zweier Punktladungen nach der WellenmechanikThe European Physical Journal A, 1928