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American Physical Society, Physical Review Letters, 1(102), 2009

DOI: 10.1103/physrevlett.102.011601

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Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree

Journal article published in 2009 by Ulrich D. Jentschura, Andrey Surzhykov ORCID, Jean Zinn-Justin
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This paper is available in a repository.

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Abstract

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 behaviour 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. ; Comment: 5 pages, RevTeX