Bender, Carl M. and Weniger, Ernst Joachim (2001) Numerical evidence that the perturbation expansion for a non-Hermitian PT-symmetric Hamiltonian is Stieltjes. JOURNAL OF MATHEMATICAL PHYSICS, 42 (5). pp. 2167-2183. ISSN 0022-2488
Full text not available from this repository. (Request a copy)Abstract
Recently, several studies of non-Hermitian Hamiltonians having PT symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian Hamiltonians. This paper presents further evidence of the similarity of these Hamiltonians to Hermitian Hamiltonians by examining the summation of the divergent weak-coupling perturbation series for the ground-state energy of the PT-symmetric Hamiltonian H=p(2) + 1/4 x(2)+i lambdax(3) recently studied by Bender and Dunne. For this purpose the first 193 (nonzero) coefficients of the Rayleigh-Schrodinger perturbation series in powers of lambda (2) for the ground-state energy were calculated. Pade-summation and Pade-prediction techniques recently described by Weniger are applied to this perturbation series. The qualitative features of the results obtained in this way are indistinguishable from those obtained in the case of the perturbation series for the quartic anharmonic oscillator, which is known to be a Stieltjes series. (C) 2001 American Institute of Physics.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | QUANTUM-FIELD THEORY; GROUND-STATE ENERGY; PADE-APPROXIMANT PREDICTIONS; COMPLEX PERIODIC POTENTIALS; OCTIC ANHARMONIC-OSCILLATOR; HIGGS DECAY-RATES; LARGE-ORDER; SEQUENCE TRANSFORMATIONS; EPSILON-ALGORITHM; COEFFICIENTS; |
| Subjects: | 500 Science > 540 Chemistry & allied sciences |
| Divisions: | Chemistry and Pharmacy > Institut für Physikalische und Theoretische Chemie |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Feb 2022 06:07 |
| Last Modified: | 01 Feb 2022 06:07 |
| URI: | https://pred.uni-regensburg.de/id/eprint/41464 |
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