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arXiv · hep-ph/0405279

Instantons in Quantum Mechanics and Resurgent Expansions

Ulrich D. Jentschura·Jean Zinn-Justin
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Abstract

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.

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Ulrich D. Jentschura, Jean Zinn-Justin. 2004-07-01. Instantons in Quantum Mechanics and Resurgent Expansions. https://doi.org/10.1016/j.physletb.2004.06.077

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