Summation of strongly divergent perturbation series
- 1 December 1984
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 25 (12) , 3492-3496
- https://doi.org/10.1063/1.526118
Abstract
A new method for summing strongly divergent perturbation series is presented. It is based on the change of the power series into a convergent sequence by means of an order-dependent mapping obtained from a simple scaling relation. The perturbation expansions for a one-dimensional integral and for the ground states of the anharmonic oscillator and of the linear confining potential model are accurately summed in the most unfavorable strong-coupling limit.Keywords
This publication has 21 references indexed in Scilit:
- Comments about energies of parameter-dependent systemsPhysical Review A, 1983
- Some extensions of the renormalised series approachJournal of Physics A: General Physics, 1982
- High-order perturbation theory of the imaginary part of the resonance eigenvalues of the Stark effect in hydrogen and of the anharmonic oscillator with negative anharmonicityPhysical Review A, 1981
- Renormalised perturbation seriesJournal of Physics A: General Physics, 1981
- Solutional method for the energies of a parameter-dependent systemPhysical Review A, 1979
- General anharmonic oscillatorsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- Resonances in Stark effect and perturbation theoryCommunications in Mathematical Physics, 1978
- The anharmonic oscillatorProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- Atoms in high magnetic fields (white dwarfs)Reports on Progress in Physics, 1977
- Coupling constant analyticity for the anharmonic oscillatorAnnals of Physics, 1970