ISSN:
1432-2234
Keywords:
Asymptotic expansion
;
JWKB
;
Perturbation theory
;
Borel summation
;
LoSurdo Stark effect
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
Notes:
Abstract Divergent asymptotic expansions in quantum chemistry often must be evaluated on Stokes lines, where the form of the expansion changes discontinuously and might appear to be ambiguous. Towards clarifying the use of asymptotic expansions on Stokes lines we discuss by numerical example the Airy function Bi(x) for real, positive x. Two physical problems to which this example is relevant, among others, are the Rayleigh-Schrödinger perturbation theory for the LoSurdo-Stark effect in hydrogen and the JWKB connection-formula problem, for which real series are associated with complex sums. The various roles of partial summation, Padé approximants, and Borel summation are compared. In addition, a derivation is given for an integral that occurs in a simple proof of the Borel summability of asymptotic expansions for the confluent hypergeometric function, which function is fundamental to certain quantum chemistry problems, and which integral is given incorrectly in several standard references.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00528197
Permalink
