Unified Treatment of Even and Odd Anharmonic Oscillators of Arbitrary Degree

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 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.

5 pages, RevTeX

Cited by in corpus (8)

• Physics counterpart of the PT non-hermitian tight-binding chain
• From Generalized Dirac Equations to a Candidate for Dark Energy
• Y-System and Deformed Thermodynamic Bethe Ansatz
• Non-Hermitian description of the dynamics of inter-chain pair tunnelling
• Two-Loop Corrections to the Large-Order Behavior of Correlation Functions in the One-Dimensional N-Vector Model
• Quantum Electrodynamics of Dicke States: Resonant One-Photon Exchange and Entangled Decay Rate
• Neutrino Pair Cerenkov Radiation for Tachyonic Neutrinos
• Scattering by infinitely rising one-dimensional potentials