Calculating resonance positions and widths using the Siegert approximation method

TL;DR

This paper introduces the Siegert approximation method for calculating resonance positions and widths in quantum systems, providing an intuitive approach for both linear and nonlinear Schrödinger equations.

Contribution

It presents a new, easily applicable method for analytical and numerical computation of complex resonances, complementing existing complex plane and semiclassical techniques.

Findings

Effective calculation of resonance states in quantum tunneling.

Applicable to both linear and nonlinear Schrödinger equations.

Provides an intuitive alternative to traditional methods.

Abstract

Here we present complex resonance states (or Siegert states), that describe the tunneling decay of a trapped quantum particle, from an intuitive point of view which naturally leads to the easily applicable Siegert approximation method that can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear Schr\"odinger equation. Our approach thus complements other treatments of the subject that mostly focus on methods based on continuation in the complex plane or on semiclassical approximations.