Continuation of the Stieltjes Series to the Large Regime by Finite-part Integration
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916090563526656 |
|---|---|
| author | Tica, Christian D. Galapon, Eric A. |
| author_facet | Tica, Christian D. Galapon, Eric A. |
| contents | We devise a prescription to utilize a novel convergent expansion in the strong-asymptotic regime for the Stieltjes integral and its generalizations [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to sum the associated divergent series of Stieltjes across all asymptotic regimes. The novel expansion makes use of the divergent negative-power moments which we treated as Hadamard's finite part integrals. The result allowed us to compute the ground-state energy of the quartic, sextic anharmonic oscillators as well as the $\mathcal{PT}$ symmetric cubic oscillator, and the funnel potential across all perturbation regimes from a single expansion that is built from the divergent weak-coupling perturbation series and incorporates the known leading-order strong-coupling behavior of the spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03891 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Continuation of the Stieltjes Series to the Large Regime by Finite-part Integration Tica, Christian D. Galapon, Eric A. Mathematical Physics Quantum Physics We devise a prescription to utilize a novel convergent expansion in the strong-asymptotic regime for the Stieltjes integral and its generalizations [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to sum the associated divergent series of Stieltjes across all asymptotic regimes. The novel expansion makes use of the divergent negative-power moments which we treated as Hadamard's finite part integrals. The result allowed us to compute the ground-state energy of the quartic, sextic anharmonic oscillators as well as the $\mathcal{PT}$ symmetric cubic oscillator, and the funnel potential across all perturbation regimes from a single expansion that is built from the divergent weak-coupling perturbation series and incorporates the known leading-order strong-coupling behavior of the spectra. |
| title | Continuation of the Stieltjes Series to the Large Regime by Finite-part Integration |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2302.03891 |