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arXiv · 0901.4964

Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree

U. D. Jentschura·A. Surzhykov·J. Zinn-Justin
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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.

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U. D. Jentschura, A. Surzhykov, J. Zinn-Justin. 2009-01-30. Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree. https://doi.org/10.1103/physrevlett.102.011601

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