Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree

Details Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree

2009-01-30

arxiv.org/abs/0901.4964v1

Phys.Rev.Lett. 102 (2009) 011601

Physics

Mathematical Physics

5 pages, RevTeX

Scientific paper

10.1103/PhysRevLett.102.011601

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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