Large-order perturbation theory for a non-Hermitian PT-symmetric Hamiltonian
- Department of Physics, Washington University, St. Louis, Missouri 63130 (United States)
- 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, Vol. 40, Issue 10; Other Information: PBD: Oct 1999
- Country of Publication:
- United States
- Language:
- English
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