Hydrogenic atoms in the external potential V(r)=gr+λr2: exact solutions and ground-state eigenvalue bounds using moment methods
- 1 February 1987
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 20 (2) , 419-428
- https://doi.org/10.1088/0305-4470/20/2/027
Abstract
An infinite number of exact solutions for the ground and excited states of an s-wave hydrogenic atom with the perturbation V(r)= gr+ lambda r2 are constructed, subject to special relations between g, lambda and the nuclear charge Z. A powerful method of Stieltjes moments is employed to generate rapidly converging upper and lower bounds to the ground-state energy E0(Z, g, lambda ) for arbitrary g, Z and positive lambda . The accuracies of these bounds are relatively insensitive to the strength of the perturbation. The moment method also generates the exact s-wave ground-state solutions mentioned above.Keywords
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