Large-order perturbation theory for a non-Hermitian PT-symmetric Hamiltonian

Journal Article · Fri Oct 01 04:00:00 EDT 1999 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532991· OSTI ID:689945

Bender, C M ^[1]; Dunne, G V ^[2]

---

1. Department of Physics, Washington University, St. Louis, Missouri 63130 (United States)
2. Department of Physics, University of Connecticut, Storrs, Connecticut 06269 (United States)

A precise calculation of the ground-state energy of the complex PT-symmetric Hamiltonian H=p{sup 2}+ (1) /(4) x{sup 2}+i{lambda}x{sup 3}, is performed using high-order Rayleigh{endash}Schr{umlt o}dinger perturbation theory. The energy spectrum of this Hamiltonian has recently been shown to be real using numerical methods. Here we present convincing numerical evidence that the Rayleigh{endash}Schr{umlt o}dinger perturbation series is Borel summable, and show that Pad{acute e} summation provides excellent agreement with the real energy spectrum. Pad{acute e} analysis provides strong numerical evidence that the once-subtracted ground-state energy considered as a function of {lambda}{sup 2} is a Stieltjes function. The analyticity properties of this Stieltjes function lead to a dispersion relation that can be used to compute the imaginary part of the energy for the related real but unstable Hamiltonian H=p{sup 2}+ (1) /(4) &hthinsp;x{sup 2}{minus}{epsilon}x{sup 3}. {copyright} {ital 1999 American Institute of Physics.}

• OSTI ID: 689945
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 40; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DISPERSION RELATIONS
HAMILTONIANS
PADE APPROXIMATION
PERTURBATION THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
RAYLEIGH-SCHROEDINGER FORMULA