Generalized Discrete‐Continuum Radial Integrals with Coulomb Functions

Simple closed‐form computational formulas involving only elementary functions are obtained for the hydrogenic, discrete‐continuum matrix elements . The results allow for different effective charge parameters Z and Z′ for the discrete and continuum functions. The central radial integral computed is s...

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Bibliographic Details
Published in:Journal of mathematical physics 1966-06, Vol.7 (6), p.955-959
Main Author: Bebb, H. Barry
Format: Article
Language:English
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Summary:Simple closed‐form computational formulas involving only elementary functions are obtained for the hydrogenic, discrete‐continuum matrix elements . 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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1705008