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 [script P][script T] 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.
U. D. Jentschura et al., "Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree," Physical Review Letters, American Physical Society (APS), Jan 2009.
The definitive version is available at https://doi.org/10.1103/PhysRevLett.102.011601
Keywords and Phrases
Anharmonic Oscillators; Arbitrary Levels; Dispersion relations
Article - Journal
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