Weniger, Ernst Joachim (1996) A convergent renormalized strong coupling perturbation expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator. ANNALS OF PHYSICS, 246 (1). pp. 133-165. ISSN 0003-4916, 1096-035X
Full text not available from this repository.Abstract
The Rayleigh-Schrodinger perturbation series for the energy eigenvalue of an anharmonic oscillator defined by the Hamiltonian (H) over cap((m))(beta) = (p) over cap(2) + (x) over cap(2) + beta (x) over cap(2m) with m = 2, 3, 4, ... diverges quite strongly for every beta not equal 0 and has to summed to produce numerically useful results. However, a divergent weak coupling expansion of that kind cannot be summed effectively if the coupling constant beta is large. A renormalized strong coupling expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator is constructed on the basis of a renormalization scheme introduced by F. Vinette and J. Cizek [J. Math. Phys. 32 (1991), 3392]. This expansion, which is a power series in a new effective coupling constant with a bounded domain, permits a convenient computation of the ground state energy in the troublesome strong coupling regime. It can be proven rigorously that the new expansion converges if the coupling constant is sufficiently large. Moreover, there is strong evidence that it converges for all physically relevant beta is an element of [0, infinity). The coefficients of the new expansion are defined by divergent series which can be summed efficiently with the help of a sequence transformation which uses explicit remainder estimates [E. J. Weniger, Comput. Phys. Rep. 10 (1989), 189]. (C) 1996 Academic Press, Inc.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | QUANTUM-THEORY; LARGE-ORDER; SERIES; SUMMATION; SUMMABILITY |
| Subjects: | 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 11:05 |
| Last Modified: | 07 Nov 2023 11:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/51923 |
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