### 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.

Original language | English |
---|---|

Pages (from-to) | 138-144 |

Number of pages | 7 |

Journal | Physics Letters B |

Volume | 596 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Aug 19 2004 |

### Fingerprint

### Keywords

- 11.10.Jj
- 11.15.Bt
- Asymptotic problems and properties
- General properties of perturbation theory

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physics Letters B*,

*596*(1-2), 138-144. https://doi.org/10.1016/j.physletb.2004.06.077

**Instantons in quantum mechanics and resurgent expansions.** / Jentschura, U.; Zinn-Justin, Jean.

Research output: Contribution to journal › Article

*Physics Letters B*, vol. 596, no. 1-2, pp. 138-144. https://doi.org/10.1016/j.physletb.2004.06.077

}

TY - JOUR

T1 - Instantons in quantum mechanics and resurgent expansions

AU - Jentschura, U.

AU - Zinn-Justin, Jean

PY - 2004/8/19

Y1 - 2004/8/19

N2 - 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.

AB - 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.

KW - 11.10.Jj

KW - 11.15.Bt

KW - Asymptotic problems and properties

KW - General properties of perturbation theory

UR - http://www.scopus.com/inward/record.url?scp=3843061124&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3843061124&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2004.06.077

DO - 10.1016/j.physletb.2004.06.077

M3 - Article

AN - SCOPUS:3843061124

VL - 596

SP - 138

EP - 144

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 1-2

ER -