Multi-instantons and exact results III: Unification of even and odd anharmonic oscillators

Journal Article · Sat May 15 04:00:00 EDT 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.01.002· OSTI ID:21336130

Surzhykov, Andrey ^[1]; Zinn-Justin, Jean ^[2]

---

1. Physikalisches Institut der Universitaet, Philosophenweg 12, 69120 Heidelberg (Germany)
2. CEA, IRFU and Institut de Physique Theorique, Centre de Saclay, F-91191 Gif-Sur-Yvette (France)

This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin, U.D. Jentschura, Ann. Phys. (N.Y.) 313 (2004) 197 and 269], we here focus on simple even and odd anharmonic oscillators for arbitrary magnitude and complex phase of the coupling parameter. A unification is achieved by the use of PT-symmetry inspired dispersion relations and generalized quantization conditions that include instanton configurations. Higher-order formulas are provided for the oscillators of degrees 3 to 8, which lead to subleading corrections to the leading factorial growth of the perturbative coefficients describing the resonance energies. Numerical results are provided, and higher-order terms are found to be numerically significant. The resonances are described by generalized expansions involving intertwined nonanalytic exponentials, logarithmic terms and power series. Finally, we summarize spectral properties and dispersion relations of anharmonic oscillators, and their interconnections. The purpose is to look at one of the classic problems of quantum theory from a new perspective, through which we gain systematic access to the phenomenologically significant higher-order terms.

• OSTI ID: 21336130
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 5 Vol. 325; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANHARMONIC OSCILLATORS
ASYMPTOTIC SOLUTIONS
DISPERSION RELATIONS
ENERGY LEVELS
INSTANTONS
OSCILLATORS
PERTURBATION THEORY
POWER SERIES
QUANTIZATION
RESONANCE
SYMMETRY