Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical case, the eigenvalue may be expressed in terms of a generalized perturbative expansion (resurgent expansion). Modified Bohr-Sommerfeld quantization conditions lead to generalized perturbative expansions which may be expressed in terms of nonanalytic factors of the form exp(-a/g), where a>0 is the instanton action, and power series in the coupling g, as well as logarithmic factors. The ground-state energy, for the specific Hamiltonians, is shown to be dominated by instanton effects, and we provide numerical evidence for the validity of the related conjectures.
U. D. Jentschura and J. Zinn-Justin, "Instantons in Quantum Mechanics and Resurgent Expansions," Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 596, no. 1-2, pp. 138-144, Elsevier, Aug 2004.
The definitive version is available at https://doi.org/10.1016/j.physletb.2004.06.077
Keywords and Phrases
Energy; Quantum Mechanics; Validation Process; 11.10.Jj; 11.15.Bt; Asymptotic Problems And Properties; General Properties Of Perturbation Theory
International Standard Serial Number (ISSN)
Article - Journal
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