ISSN:
0020-7608
Keywords:
Computational Chemistry and Molecular Modeling
;
Atomic, Molecular and Optical Physics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
Rayleigh-Schrouml;dinger (RS) perturbation expansions for the eigenvalues E(λ) of a hydrogen atom in the general polynomial perturbation V(r) = aλr + b〉2r2, a, b 〉 0, are studied. When a2 = 2b, the ground state energy is exactly E(λ) = -(1/2) + (3/2)a〉, i.e., the RS series is truncated. In the case a2 〉 2b, the RS series is negative Stieltjes. In general, when λ 〈 0, a well of depth ω ≈ -a2/(4b2) (note the λ independence) is situated at rω = a/(2b|λ|). When a2 〉 2b/N2, and interaction between this well and the hydrogenic state ψNLM(λ) is possible, thus creating a pair of asymptotically degenerate eigenstates separated by a “gap” δE(λ). The large order behavior of the RS coefficients ENLM(n) may be computed from the asymptotics of δE(λ), which is, in turn, related to the tunnelling integral. For excited states, stricter inequalities must be obeyed for Stieltjes behavior. The E(n)NLM may be calculated either numerically or in closed form via the “so(4, 2) Lie algebra technology” for such hydrogenic problems.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/qua.560320507
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