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Borel summability and indeterminacy of the Stieltjes moment problem: Application to the anharmonic oscillators
- 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.
- Subjects :
- Power series
Stieltjes moment problem
Mathematical analysis
Anharmonicity
Mathematics::Classical Analysis and ODEs
Statistical and Nonlinear Physics
Riemann–Stieltjes integral
Mathematics::Spectral Theory
Moment problem
Padé approximant
Finite set
Mathematical Physics
Eigenvalues and eigenvectors
Mathematical physics
Mathematics
Subjects
Details
- ISSN :
- 10897658 and 00222488
- Volume :
- 19
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Physics
- Accession number :
- edsair.doi...........bbfaab5dee62abb9e6bd232591c3c394