A strongly perturbed quantum system is a semiclassical system

TL;DR

This paper demonstrates that strongly perturbed quantum systems, which are semiclassical, exhibit eigenvalue expansions similar to WKB series, derived through duality in perturbation theory.

Contribution

It establishes a connection between perturbation series and semiclassical eigenvalue expansions using duality principles.

Findings

Eigenvalue expansions match WKB series in strongly perturbed systems

Perturbation series can be rederived via duality in perturbation theory

Semiclassical systems maintain their eigenvalue structure under strong perturbations

Abstract

We show that a strongly perturbed quantum system, being a semiclassical system characterized by the Wigner-Kirkwood expansion for the propagator, has the same expansion for the eigenvalues as for the WKB series. The perturbation series is rederived by the duality principle in perturbation theory.