Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree

Journal Article · Fri Jan 09 04:00:00 EST 2009 · Physical Review Letters

DOI:https://doi.org/10.1103/PHYSREVLETT.102.011601· OSTI ID:21180089

Jentschura, Ulrich D ^[1]; Surzhykov, Andrey ^[2]; Zinn-Justin, Jean ^[3]

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1. Department of Physics, Missouri University of Science and Technology, Rolla Missouri 65409-0640 (United States)
2. Max-Planck-Institut fuer Kernphysik, Postfach 103980, 69029 Heidelberg (Germany)
3. CEA, IRFU, and Institut de Physique Theorique, Centre de Saclay, 91191 Gif-Sur-Yvette (France)

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.

• OSTI ID: 21180089
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 1 Vol. 102; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANHARMONIC OSCILLATORS
DISPERSION RELATIONS
EXCITED STATES
INSTANTONS
PERTURBATION THEORY
POTENTIALS
QUANTIZATION
SYMMETRY