Abstract
A new compact two-range addition theorem for Coulomb Sturmians is presented. This theorem has been derived by breaking up the exponential-type orbitals into convenient elementary functions: the Yukawa potential (e − αr ∕ r) and “evenly-loaded solid harmonics,” \(({r}^{2\nu +l}{Y }_{l}^{m}(\hat{r})\) for which translation formulas are available. The resulting two-range translation formula for the exponential orbital is presented and used to construct a new addition theorem for the Coulomb Sturmians.
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Acknowledgements
This work was supported by the National Science Foundation of the United States under the CREST program’s Florida A&M University Center for Astrophysical Science and Technology.
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Gebremedhin, D.H., Weatherford, C.A. (2012). Two-Range Addition Theorem for Coulomb Sturmians. In: Hoggan, P., Brändas, E., Maruani, J., Piecuch, P., Delgado-Barrio, G. (eds) Advances in the Theory of Quantum Systems in Chemistry and Physics. Progress in Theoretical Chemistry and Physics, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2076-3_4
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DOI: https://doi.org/10.1007/978-94-007-2076-3_4
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