Complex HVPT and hyperasymptotics

Abstract

Complex hypervirial perturbation theory (HVPT) is applied to the problem of a harmonic oscillator with a perturbation gx3exp(iφ), for which the traditional Rayleigh–Schodinger perturbation theory has to be supplemented by hyperasymptotics for obtaining accurate resonance energies in the negative φ region. Complex HVPT gives accurate results for positive φ and for negative φ up to about . The case of a quartic perturbed oscillator is also treated.