Unified treatment of even and odd anharmonic oscillators of arbitrary degree

Ulrich D. Jentschura, Andrey Surzhykov, Jean Zinn-Justin

Research output: Contribution to journalArticle

25 Citations (Scopus)


We present a unified treatment, including higher-order corrections, of anharmonic oscillators of arbitrary even and odd degree. Our approach is based on a dispersion relation which takes advantage of the PT symmetry of odd potentials for imaginary coupling parameter, and of generalized quantization conditions which take into account instanton contributions. We find a number of explicit new results, including the general behavior of large-order perturbation theory for arbitrary levels of odd anharmonic oscillators, and subleading corrections to the decay width of excited states for odd potentials, which are numerically significant.

Original languageEnglish
Article number011601
JournalPhysical review letters
Issue number1
Publication statusPublished - Jan 5 2009

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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