Instantons in quantum mechanics and resurgent expansions

U. Jentschura, Jean Zinn-Justin

Research output: Contribution to journalArticle

31 Citations (Scopus)

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 languageEnglish
Pages (from-to)138-144
Number of pages7
JournalPhysics Letters B
Volume596
Issue number1-2
DOIs
Publication statusPublished - Aug 19 2004

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instantons
quantum mechanics
expansion
ground state
power series
eigenvalues
energy levels
perturbation
energy

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

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

In: Physics Letters B, Vol. 596, No. 1-2, 19.08.2004, p. 138-144.

Research output: Contribution to journalArticle

Jentschura, U. ; Zinn-Justin, Jean. / Instantons in quantum mechanics and resurgent expansions. In: Physics Letters B. 2004 ; Vol. 596, No. 1-2. pp. 138-144.
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