Borel summability: Application to the anharmonic oscillator

We prove that the energy levels of an arbitrary anharmonic oscillator ( x 2 m and in any finite number of dimensions) are determined uniquely by their Rayleigh-Schr⊙dinger series via a (generalized) Borel summability method. To use this method for computations, one must make an analytic continuation...

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Bibliographic Details
Published in:Physics letters. B 1970-01, Vol.32 (7), p.631-634
Main Authors: Graffi, S., Grecchi, V., Simon, B.
Format: Article
Language:English
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Summary:We prove that the energy levels of an arbitrary anharmonic oscillator ( x 2 m and in any finite number of dimensions) are determined uniquely by their Rayleigh-Schr⊙dinger series via a (generalized) Borel summability method. To use this method for computations, one must make an analytic continuation which we accomplish by (a rigorously unjustified) use of Padé approximants in the case of p 2 + x 2 + βx 4. The numerical results appear to be better than with the direct use of Padé approximants.
ISSN:0370-2693
1873-2445
DOI:10.1016/0370-2693(70)90564-2