Semiclassical resonance asymptotics for the delta potential on the half line

TL;DR

This paper derives asymptotic formulas for resonances in a quantum model with a delta potential on the half-line, using Lambert W function expansions, relevant for physical systems like quantum corrals.

Contribution

It introduces a novel approach to compute resonance asymptotics for the delta potential using Lambert W function series expansions.

Findings

Resonance widths are expressed explicitly via Lambert W function.

Asymptotic formulas match physical models of thin barriers.

Applicable to quantum corrals and leaky quantum graphs.

Abstract

We compute resonance width asymptotics for the delta potential on the half-line, by deriving a formula for resonances in terms of the Lambert W function and applying a series expansion. This potential is a simple model of a thin barrier, motivated by physical problems such as quantum corrals and leaky quantum graphs.