Cizek, Jiří and Weniger, Ernst Joachim and Bracken, Paul and Spirko, Vladimir (1996) Effective characteristic polynomials and two-point Pade approximants as summation techniques for the strongly divergent perturbation expansions of the ground state energies of anharmonic oscillators. PHYSICAL REVIEW E, 53 (3). pp. 2925-2939. ISSN 2470-0045, 2470-0053
Full text not available from this repository.Abstract
Pade approximants are able to sum effectively the Rayleigh-Schrodinger perturbation series for the ground state energy of the quartic anharmonic oscillator, as well as the corresponding renormalized perturbation expansion [E.J. Weniger, J. Cizek, and F. Vinette, J. Math. Phys. 34, 571 (1993)]. In the sextic case, Pade approximants are still able to sum these perturbation series, but convergence is so slow that they are computationally useless. In the octic case, Pade approximants are not powerful enough and fail. On the other hand, the inclusion of only a few additional data from the strong coupling domain [E.J. Weniger, Ann. Phys. (N.Y.) (to be published)] greatly enhances the power of summation methods. The summation techniques that we consider are two-point Pade approximants and effective characteristic polynomials. It is shown that these summation methods give good results for the quartic and sextic anharmonic oscillators, and even in the case of the octic anharmonic oscillator, which represents an extremely challenging summation problem, two-point Pade approximants give relatively good results.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | STRONG-COUPLING EXPANSION; LARGE-ORDER; QUANTUM-THEORY; SERIES; SUMMABILITY |
| Subjects: | 500 Science > 530 Physics 500 Science > 540 Chemistry & allied sciences |
| Divisions: | Chemistry and Pharmacy > Institut für Physikalische und Theoretische Chemie |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Nov 2023 10:27 |
| Last Modified: | 07 Nov 2023 10:27 |
| URI: | https://pred.uni-regensburg.de/id/eprint/51904 |
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