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Perturbation theory of odd anharmonic oscillators

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Abstract

We study the perturbation theory forH=p 2+x 2+βx 2n+1,n=1, 2, .... It is proved that when Imβ≠0,H has discrete spectrum. Any eigenvalue is uniquely determined by the (divergent) Rayleigh-Schrödinger perturbation expansion, and admits an analytic continuation to Imβ=0 where it can be interpreted as a resonance of the problem.

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Authors and Affiliations

  1. Istituto Matematico, Università di Modena, I-41100, Modena, Italy

    E. Caliceti, S. Graffi & M. Maioli

Authors
  1. E. Caliceti
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  2. S. Graffi
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  3. M. Maioli
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Additional information

Communicated by J. Ginibre

Partially supported by G.N.F.M., C.N.R.

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Caliceti, E., Graffi, S. & Maioli, M. Perturbation theory of odd anharmonic oscillators. Commun.Math. Phys. 75, 51–66 (1980). https://doi.org/10.1007/BF01962591

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  • DOI: https://doi.org/10.1007/BF01962591

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