Differential equation for the spherical dipole matrix elements of hydrogen
- 1 September 1990
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 42 (5) , 2555-2561
- https://doi.org/10.1103/physreva.42.2555
Abstract
A differential equation in l for hydrogenic radial dipole matrix elements is generated from the recursion relations of Infeld and Hull [Rev. Mod. Phys. 23, 31 (1951)]. The equation is valid for all (n,n’)≫1, for all ‖Δn‖ieq‖n’-n‖, and for bound-free transitions from excited states. Approximate solutions are obtained for the case l≪n and are found to be equivalent to those of other workers when ‖Δn‖≫1. We also present a power-series solution in l good for all ‖Δn‖. General features of the dependence of the matrix elements on l are explained.Keywords
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