Jentschura UD, Surzhykov A, Zinn-Justin J. Unified treatment of even and odd anharmonic oscillators of arbitrary degree.
PHYSICAL REVIEW LETTERS 2009;
102:011601. [PMID:
19257178 DOI:
10.1103/physrevlett.102.011601]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2008] [Indexed: 05/27/2023]
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 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.
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