English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Recently, several studies of non-Hermitian Hamiltonians having $\mathcal{PT}$symmetry have been conducted. Most striking about these complex Hamiltonians ishow closely their properties resemble those of conventional HermitianHamiltonians. This paper presents further evidence of the similarity of theseHamiltonians to Hermitian Hamiltonians by examining the summation of thedivergent weak-coupling perturbation series for the ground-state energy of the$\mathcal{PT}$-symmetric Hamiltonian $H=p^2+{1/4}x^2+i\lambda x^3$ recentlystudied by Bender and Dunne. For this purpose the first 193 (nonzero)coefficients of the Rayleigh-Schr\"odinger perturbation series in powers of$\lambda^2$ for the ground-state energy were calculated. Pad\'e-summation andPad\'e-prediction techniques recently described by Weniger are applied to thisperturbation series. The qualitative features of the results obtained in thisway are indistinguishable from those obtained in the case of the perturbationseries for the quartic anharmonic oscillator, which is known to be a Stieltjesseries.Comment: 20 pages, 0 figure

Numerical evidence that the perturbation expansion for a non-Hermitian PT-symmetric Hamiltonian is Stieltjes