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Borel summability and indeterminacy of the Stieltjes moment problem: Application to the anharmonic oscillators

Authors :
Vincenzo Grecchi
Sandro Graffi
Source :
Journal of Mathematical Physics. 19:1002-1006
Publication Year :
1978
Publisher :
AIP Publishing, 1978.

Abstract

An indeterminacy criterion is proven for the moment problem associated with the coefficients of a Borel summable power series of Stieltjes type which diverge faster than (2n) !. As an application we show that the Stieltjes type continued fraction corresponding to the Rayleigh–Schrodinger perturbation expansions for the energy eigenvalues of the anharmonic oscillators (x2(m+1) and in any finite number of dimensions) does not converge to the eigenvalues if m≳2. In particular, this implies the nonconvergence of the Pade approximants to the eigenvalues of p2+x2+λx2(m+1) if m≳2.

Details

ISSN :
10897658 and 00222488
Volume :
19
Database :
OpenAIRE
Journal :
Journal of Mathematical Physics
Accession number :
edsair.doi...........bbfaab5dee62abb9e6bd232591c3c394